Table of contents

We show that, in analyzing differential equations obeyed by one-loop gauge theory amplitudes, one must take into account a certain holomorphic anomaly. When this is done, the results are consistent with the simplest twistor-space picture of the available one-loop amplitudes.

We systematically study the most general Lorentz-violating graviton mass invariant under three-dimensional Eucledian group. We find that at general values of mass parameters the massive graviton has six propagating degrees of freedom, and some of them are ghosts or lead to rapid classical instabilities. However, there is a number of different regions in the mass parameter space where massive gravity is described by a consistent low-energy effective theory with cutoff ∼ (mM_Pl)^1/2. This theory is free of rapid instabilities and vDVZ discontinuity. Each of these regions is characterized by certain fine-tuning relations between mass parameters, generalizing the Fierz–Pauli condition. In some cases the required fine-tunings are consequences of the existence of the subgroups of the diffeomorphism group that are left unbroken by the graviton mass. We found two new cases, when the resulting theories have a property of UV insensitivity, i.e. remain well behaved after inclusion of arbitrary higher dimension operators without assuming any fine-tunings among the coefficients of these operators, besides those enforced by the symmetries. These theories can be thought of as generalizations of the ghost condensate model with a smaller residual symmetry group. We briefly discuss what kind of cosmology can one expect in massive gravity and argue that the allowed values of the graviton mass may be quite large, affecting growth of primordial perturbations, structure formation and, perhaps, enhancing the backreaction of inhomogeneities on the expansion rate of the Universe.

We discuss the computation of correlation functions in holographic RG flows. The method utilizes a recently developed hamiltonian version of holographic renormalization and it is more efficient than previous methods. A significant simplification concerns the treatment of infinities: instead of performing a general analysis of counterterms, we develop a method where only the contribution of counterterms to any given correlators needs to be computed. For instance, the computation of renormalized 2-point functions requires only an analysis at the linearized level. We illustrate the method by discussing flat and AdS-sliced domain walls. In particular, we discuss correlation functions of the Janus solution, a recently discovered non-supersymmetric but stable AdS-sliced domain wall.

We analyze the twistor space structure of certain one-loop amplitudes in gauge theory. For some amplitudes, we find decompositions that make the twistor structure manifest; for others, we explore the twistor space structure by finding differential equations that the amplitudes obey.

We give a full account of the Numerical Stochastic Perturbation Theory method for Lattice Gauge Theories. Particular relevance is given to the inclusion of dynamical fermions, which turns out to be surprisingly cheap in this context. We analyse the underlying stochastic process and discuss the convergence properties. We perform some benchmark calculations and—as a byproduct—we present original results for Wilson loops and the 3-loop critical mass for Wilson fermions.

In this work quantum physics in noncommutative spacetime is developed. It is based on the work of Doplicher et al. which allows for time-space noncommutativity. The Moyal plane is treated in detail. In the context of noncommutative quantum mechanics, some important points are explored, such as the formal construction of the theory, symmetries, causality, simultaneity and observables. The dynamics generated by a noncommutative Schrödinger equation is studied. We prove in particular the following: suppose the hamiltonian H of a quantum mechanical particle on spacetime ^N−1 × has no explicit time dependence, and the spatial coordinates commute in its noncommutative form (the only noncommutativity being between time and a space coordinate). Then the noncommutative version Ĥ of H and H have identical spectra.

A range of bosonic models can be expressed as (sometimes generalized) σ-models, with equations of motion coming from a selfduality constraint. We show that in D = 2, this is easily extended to supersymmetric cases, in a superspace approach. In particular, we find that the configurations of fields of a superconformal / coset models which satisfy some selfduality constraint are automatically solutions to the equations of motion of the model. Finally, we show that symmetric space σ-models can be seen as infinite-dimensional / models constrained by a selfduality equation, with the loop extension of and a maximal subgroup. It ensures that these models have a hidden global symmetry together with a local gauge symmetry.

In this paper we discuss how the peculiar properties of twisted mass lattice QCD at maximal twist can be employed to set up a consistent computational scheme in which, despite the explicit breaking of chiral symmetry induced by the presence of the Wilson and mass terms in the action, it is possible to completely bypass the problem of wrong chirality and parity mixings in the computation of the CP-conserving matrix elements of the ΔS = 1,2 effective weak hamiltonian, and at the same time have a positive determinant for pairs of non-degenerate quarks, as well as absence of O(a) discretization effects in on-shell quantities with no need of improving lattice action and operators.

We construct effective field theories in which gravity is modified via spontaneous breaking of local Lorentz invariance. This is a gravitational analogue of the Higgs mechanism. These theories possess additional graviton modes and modified dispersion relations. They are manifestly well-behaved in the UV and free of discontinuities of the van Dam-Veltman-Zakharov type, ensuring compatibility with standard tests of gravity. They may have important phenomenological effects on large distance scales, offering an alternative to dark energy. For the case in which the symmetry is broken by a vector field with the wrong sign mass term, we identify four massless graviton modes (all with positive-definite norm) and show the absence of the discontinuity.

Abelian gerbes and twisted bundles describe the topology of the NS 3-form gauge field strength H. We review how they have been usefully applied to study and resolve global anomalies in open string theory. Abelian 2-gerbes and twisted nonabelian gerbes describe the topology of the 4-form field strength G of M-theory. We show that twisted nonabelian gerbes are relevant in the study and resolution of global anomalies of multiple coinciding M5-branes. Global anomalies for one M5-brane have been studied by Witten and by Diaconescu, Freed and Moore. The structure and the differential geometry of twisted nonabelian gerbes (i.e. modules for 2-gerbes) is defined and studied. The nonabelian 2-form gauge potential living on multiple coinciding M5-branes arises as curving (curvature) of twisted nonabelian gerbes. The nonabelian group is in general E₈, the central extension of the E₈ loop group. The twist is in general necessary to cancel global anomalies due to the nontriviality of the 11-dimensional 4-form field strength G and due to the possible torsion present in the cycles the M5-branes wrap. Our description of M5-branes global anomalies leads to the D4-branes one upon compactification of M-theory to Type IIA theory.

We construct T-parity invariant extensions of the littlest Higgs model, in which only linear representations of the full symmetry group are employed, without recourse to the non-linear representations introduced by Coleman, Callan, Wess, and Zumino (CCWZ). These models are based on the symmetry breaking pattern SU(5)_l × H_r/SO(5), where H_r can be SO(5) or other larger symmetry groups. The structure of the models in the SU(5)_l sector is identical to the littlest Higgs model based on SU(5)/SO(5). Since the full symmetry group is realized linearly, these models can be thought of as possible UV extensions of the T-invariant model using non-linear representations via CCWZ, with whom they share similar low energy phenomenology. We also comment on how to avoid constraints from four-fermion operators on T-invariant models with or without CCWZ construction. The electroweak data therefore place a very weak bound on the symmetry breaking scale, f ⩾ 450 GeV.

Supersymmetric grand unified models based on the gauge group SO(10) are especially attractive in light of recent data on neutrino masses. The simplest SO(10) SUSY GUT models predict unification of third generation Yukawa couplings in addition to the usual gauge coupling unification. Recent surveys of Yukawa unified SUSY GUT models predict an inverted scalar mass hierarchy in the spectrum of sparticle masses if the superpotential μ term is positive. In general, such models tend to predict an overabundance of dark matter in the universe. We survey several solutions to the dark matter problem in Yukawa unified supersymmetric models. One solution—lowering the GUT scale mass value of first and second generation scalars—leads to _R and _R squark masses in the 90-120 GeV regime, which should be accessible to Fermilab Tevatron experiments. We also examine relaxing gaugino mass universality which may solve the relic density problem by having neutralino annihilations via the Z or h resonances, or by having a wino-like LSP.

The nonperturbative 1→N tachyon scattering amplitude in 2D type 0A string theory is computed. The probability that N particles are produced is a monotonically decreasing function of N whenever N is large enough that statistical methods apply. The results are compared with expectations from black hole thermodynamics.

The physical states of = 4 conformal supergravity in four dimensions occur in twistor-string theory by Berkovits and Witten [1]. We study two alternative versions of twistor-string theory based on the B-model of weighted projective space WCP^3|2 and based on a certain construction involving open strings. The spacetime fields described by the twistor superfields contain the physical states of = 1 conformal supergravity from above = 4 superspace approach.

Field theory and gauge theory on noncommutative spaces have been established as their own areas of research in recent years. The hope prevails that a noncommutative gauge theory will deliver testable experimental predictions and will thus be a serious candidate for an extension of the Standard Model. This note contains the results for expanded gauge theory actions on a noncommutative space with constant θ^μν, up to second order, together with a discussion of the ambiguities of the expanded theory and how they affect the action.

Polarized parton distributions and structure functions of the nucleon are analyzed in the improved valon model. The valon representation provides a model to represent hadrons in terms of quarks, providing a unified description of bound state and scattering properties of hadrons. Polarized valon distributions are seen to play an important role in describing the spin dependence of parton distributions in the leading order (LO) and next-to-leading order (NLO) approximations. In the polarized case, a convolution integral is derived in the framework of the valon model. The Polarized valon distribution in a proton and the polarized parton distributions inside the valon are necessary to obtain the polarized parton distributions in a proton. Bernstein polynomial averages are used to extract the unknown parameters of the polarized valon distributions by fitting to the available experimental data. The predictions for the NLO calculations of the polarized parton distributions and proton structure functions are compared with the LO approximation. It is shown that the results of the calculations for the proton structure function, xg₁^p, and its first moment, Γ₁^p, are in good agreement with the experimental data for a range of values of Q². Finally the spin contribution of the valons to the proton is calculated.

In this paper we consider (n+1)-dimensional cosmological model with scalar field and antisymmetric (p+2)-form. Using an electric composite Sp-brane ansatz the field equations for the original system reduce to the equations for a Toda-like system with n(n−1)/2 quadratic constraints on the charge densities. For certain odd dimensions (D = 4m+1 = 5,9,13,...) and (p+2)-forms (p = 2m−1 = 1,3,5,...) these algebraic constraints can be satisfied with the maximal number of charged branes (i.e. all the branes have non-zero charge densities). These solutions are characterized by self-dual or anti-self-dual charge density forms Q (of rank 2m). For these algebraic solutions with the particular D, p, Q and non-exceptional dilatonic coupling constant λ we obtain general cosmological solutions to the field equations and some properties of these solutions are highlighted (e.g. Kasner-like behavior, the existence of attractor solutions). We prove the absence of maximal configurations for p = 1 and even D (e.g. for D = 10 supergravity models and those of superstring origin).

We discuss non-compact SL(2,) sectors in N=4 SYM and in AdS string theory and compare their integrable structures. We formulate and solve the Riemann-Hilbert problem for the finite gap solutions of the classical sigma model and show that at one loop it is identical to the classical limit of Bethe equations of the spin (-1/2) chain for the dilatation operator of SYM.

From the SU(2) spin chain sigma model at the one-loop and two-loop orders we recover the classical circular string solution with two S⁵ spins (J₁,J₂) in the AdS₅ × S⁵ string theory. In the SL(2) sector of the one-loop spin chain sigma model we explicitly construct a solution which corresponds to the folded string solution with one AdS₅ spin S and one S⁵ spin J. In the one-loop general sigma model we demonstrate that there exists a solution which reproduces the energy of the circular constant-radii string solution with three spins (S₁,S₂,J).

Consequences of a new force mediated by a light scalar particle for neutrino oscillation experiments are considered. Such a force could give rise to neutrino masses and mixings whose matter dependence for earth densities is much more significant than the MSW effect. We consider the effects of such a new force on the limits derived from oscillation experiments, and examine how the constraints on neutrino models are altered. Re-analysis of neutrino data, as well as new experiments in which large matter effects are systematically explored, is required to directly probe such physics beyond the standard model.

We analyze observational constraints on the parameter space of tachyonic inflation with a gaussian potential and discuss some predictions of this scenario. As was shown by Kofman and Linde, it is extremely problematic to achieve the required range of parameters in conventional string compactifications. We investigate if the situation can be improved in more general compactifications with a warped metric and a varying dilaton. The simplest examples are the warped throat geometries that arise in the vicinity of of a large number of space-filling D-branes. We find that the parameter range for inflation can be accommodated in the background of D6-branes wrapping a three-cycle in type-IIA. We comment on the requirements that have to be met in order to realize this scenario in an explicit string compactification.

We study the Fayet-Iliopoulos (FI) D-terms on D-branes in type-II Calabi-Yau backgrounds. We provide a simple worldsheet proof of the fact that, at tree level, these terms only couple to scalars in closed string hypermultiplets. At the one-loop level, the D-terms get corrections only if the gauge group has an anomalous spectrum, with the anomaly cancelled by a Green-Schwarz mechanism. We study the local type-IIA model of D6-branes at SU(3) angles and show that, as in field theory, the one-loop correction suffers from a quadratic divergence in the open string channel. By studying the closed string channel, we show that this divergence is related to a closed string tadpole, and is cancelled when the tadpole is cancelled. Next, we study the cosmic strings that arise in the supersymmetric phases of these systems in light of recent work of Dvali et al. In the type-IIA intersecting D6-brane examples, we identify the D-term strings as D4-branes ending on the D6-branes. Finally, we use = 1 dualities to relate these results to previous work on the FI D-term of heterotic strings.

One-loop matching corrections are calculated for Soft-Collinear Effective Theory (SCET) operators relevant to the analysis of heavy-to-light meson form factors at large recoil. The numerical impact of radiative corrections on form factor predictions is assessed. Evanescent operators in the effective theory are studied and it is shown that even in problems of the Sudakov type, these operators can be renormalized to have vanishing matrix elements.

We present solutions in six-dimensional gravity coupled to a sigma model, in the presence of three-brane sources. The space transverse to the branes is a compact non-singular manifold. The example of O(3) sigma model in the presence of two three-branes is worked out in detail. We show that the four-dimensional flatness is obtained with a single condition involving the brane tensions, which are in general different and may be both positive, and another characteristic of the branes, vorticity. We speculate that the adjustment of the effective four-dimensional cosmological constant may occur through the exchange of vorticity between the branes. We then give exact instanton type solutions for sigma models targeted on a general Kähler manifold, and elaborate in this framework on multi-instantons of the O(3) sigma model. The latter have branes, possibly with vorticities, at the instanton positions, thus generalizing our two-brane solution.

We consider the case of coherent gauge invariant operators in the SU(3) and SO(4) sectors. We argue that in many cases, these sectors can be closed in the thermodynamic limit, even at higher loops. We then use a modification of the Bethe equations which is a natural generalization of a proposal put forward by Serban and Staudacher to make gauge theory predictions for the anomalous dimensions for a certain class of operators in each sector. We show that the predictions are consistent with semiclassical string predictions at two loops but in general fail to agree at three loops. Interestingly, in both cases there is one point in the configuration space where the gauge theory and string theory predictions agree. In the SU(3) case it corresponds to a circular string with R-charge assignment (J,J,J).

We explore the full parameter space of Minimal Supergravity (mSUGRA), allowing all four continuous parameters (the scalar mass m₀, the gaugino mass m_1/2, the trilinear coupling A₀, and the ratio of Higgs vacuum expectation values tan β) to vary freely. We apply current accelerator constraints on sparticle and Higgs masses, and on the b→sγ branching ratio, and discuss the impact of the constraints on g_μ−2. To study dark matter, we apply the WMAP constraint on the cold dark matter density. We develop Markov Chain Monte Carlo (MCMC) techniques to explore the parameter regions consistent with WMAP, finding them to be considerably superior to previously used methods for exploring supersymmetric parameter spaces. Finally, we study the reach of current and future direct detection experiments in light of the WMAP constraint.

We present a mechanism for exit from inflation and reheating using the AdS/CFT correspondence. A cosmological evolution is induced on a probe D3-brane as it moves in a black D-brane background of type-0 string theory. If the tachyon field is non zero, inflation is induced on the brane-universe, with the equation of state parameter in the range −1 < w < −1/3 depending on the position of the probe brane in the bulk. As the probe brane approaches the horizon of the background black hole, the inflation rate decreases and the value of w gets larger. At some critical distance away from the horizon, inflation ends. When the brane-universe reaches the horizon, the conformal invariance is restored, the background geometry becomes AdS₅ × S⁵, and the brane-universe feels the CFT thermal radiation and reheats.

We prove the existence of global solutions to the Cauchy problem for noncommutative nonlinear wave equations in arbitrary even spatial dimensions where the noncommutativity is only in the spatial directions. We find that for existence there are no conditions on the degree of the nonlinearity provided the potential is positive. We furthermore prove that nonlinear noncommutative waves have infinite propagation speed, i.e., if the initial conditions at time 0 have a compact support then for any positive time the support of the solution can be arbitrarily large.

The Wigner phase-space distribution function provides the basis for Moyal's deformation quantization alternative to the more conventional Hilbert space and path integral quantization. In this paper, we investigate the basic aspects of deformation quantization for noncommutative quantum mechanics (NCQM). We first prove some general relations of the Weyl correspondence in non-commuting phase-space. Then we derive explicit form of the Wigner Function (WF) for NCQM starting from fundamental principle of the Weyl correspondence, and show that it satisfies a generalized ∗-genvalue equation. We also demonstrate that the new WFs possess orthonormality and completeness, so they can be used as a basis to expand all phase-space functions. Some example is discussed to support our results.

We study Landau-gauge Yang-Mills theory by means of a nonperturbative vertex expansion of the quantum effective action. Using an exact renormalization group equation, we compute the fully dressed gluon and ghost propagators to lowest nontrivial order in the vertex expansion. In the mid-momentum regime, p² ∼ (1) GeV², we probe the propagator flow with various ansätze for the three- and four-point correlations. We analyze the potential of these truncation schemes to generate a nonperturbative scale. We find universal infrared behavior of the propagators, if the gluon dressing function has developed a mass-like structure at mid-momentum. The resulting power laws in the infrared support the Kugo-Ojima confinement scenario.

Using a nested coset construction a collection of D-branes that appear to generate all the K-theory charges of string theory on SU(n) are constructed and their charges are determined.

We compute certain spinorial cohomology groups controlling possible supersymmetric deformations of eleven-dimensional supergravity up to order l³ in the Planck length. At (l) and (l²) the spinorial cohomology groups are trivial and therefore the theory cannot be deformed supersymmetrically. At (l³) the corresponding spinorial cohomology group is generated by a nontrivial element. On an eleven-dimensional manifold M such that p₁(M)≠0, this element corresponds to a supersymmetric deformation of the theory, which can only be redefined away at the cost of shifting the quantization condition of the four-form field strength.

We look for 3-dimensional Poisson-Lie dualizable sigma models that satisfy the vanishing β-function equations with constant dilaton field. Using the Poisson-Lie T-plurality we then construct 3-dimensional sigma models that correspond to various decompositions of Drinfeld double. Models with nontrivial dilaton field may appear. It turns out that for ``traceless'' dual algebras they satisfy the vanishing β-function equations as well. In certain cases the dilaton cannot be defined in some of the dual models. We provide an explanation why this happens and give criteria predicting when it happens.

A modification of the relation between axion mass and the PQ constant permits a relaxation of the astrophysical constraints, considerably enlarging the allowed axion parameter space. We develop this idea in this paper, discussing a model for an ultramassive axion, which essentially represents a supersymmetric Weinberg-Wilczek axion of the mirror world. The experimental and astrophysical limits allow a PQ scale f_a ∼ 10⁴−10⁶ GeV and a mass m_a ∼ MeV, which can be accessible for future experiments. On a phenomenological ground, such an ultramassive axion turns out to be quite interesting. It can be produced during the gravitational collapse or during the merging of two compact objects, and its subsequent decay into e⁺e⁻ provides an efficient mechanism for the transfer of the gravitational energy of the collapsing system to the electron-positron plasma. This could resolve the energy budget problem in the Gamma Ray Bursts and also help in understanding the SN type-II explosion phenomena.

The correlation function of a V−A current with a V+A current is discussed within the framework of QCD in the limit of a large number of colours N_c. Applications to the evaluation of chiral condensates of dimension six and higher, as well as to the matrix elements of the Q₇ and Q₈ electroweak penguin operators are discussed. A critical comparison with previous determinations of the same parameters has also been made.

We study cosmological defect formation that is induced by brane dynamics after brane inflation. The cosmological defects are corresponding to the branes that have less than three spacial dimensions in the uncompactified spacetime. Contrary to the previous arguments, production of monopoles and domain walls are not always negligible. Monopoles and domain walls are formed by the branes extended between mother branes.

The observational limits on the present energy density of the Universe allow for a component that redshifts like 1/a² and can contribute significantly to the total. We show that a possible origin for such a contribution is that the universe has a toroidal topology with ``wound" scalar fields around its cycles.

We study the BSFT actions by using an analytic continuation in momentum space. We compute various two- and three-point functions for some low-lying excitations including massive states on BPS/non-BPS D-branes. The off-shell two-point functions for the tachyon, the gauge field and the massive fields are found to reproduce the well-known string mass-shell conditions. We compare our action with the tachyon actions previously obtained by the derivative expansion (or the linear tachyon profiles), and find complete agreement. Furthermore, we reproduce the correct on-shell value of the tachyon-tachyon-gauge three-point function on brane-anti-brane systems. Though inclusion of the massive modes has been thought difficult because of the non-renormalizability in string σ models, we overcome this by adopting general off-shell momenta and the analytic continuation.

We explicitly construct and study the statistics of flux vacua for type-IIB string theory on an orientifold of the Calabi-Yau hypersurface ⁴_[1,1,2,2,6], parametrised by two relevant complex structure moduli. We solve for these moduli and the dilaton field in terms of the set of integers defining the 3-form fluxes and examine the distribution of vacua. We compare our numerical results with the predictions of the Ashok-Douglas density det(−−ω), finding good overall agreement in different regions of moduli space. The number of vacua are found to scale with the distance in flux space. Vacua cluster in the region close to the conifold singularity. Large supersymmetry breaking is more generic but supersymmetric and hierarchical supersymmetry breaking vacua can also be obtained. In particular, the small superpotentials and large dilaton VEVs needed to obtain de Sitter space in a controllable approximation are possible but not generic. We argue that in a general flux compactification, the rank of the gauge group coming from D3 branes could be statistically preferred to be very small.

Flavour changing neutral current decays are a very sensitive test of the standard model and its extensions. In particular the decay K→πν constitutes a clean way to provide constraints, independent of long distance effects. Motivated by the recent experimental data of the E787 and E865 collaborations and by the difference between the standard model prediction and data, we consider in detail new physics scenarios such as the minimal supersymmetric standard model and R-parity violating supersymmetry. We begin with analyzing the impact of new measurements on the standard model result obtaining B(K⁺→π⁺ν) = (8.18±1.22) × 10⁻¹¹. Predictions for other rare kaon decays are discussed, too. Our results allow to improve the limits on R-parity violating couplings with respect to previous analyses.

We compute the prepotential for gauge theories descending from = 4 SYM via quiver projections and mass deformations. This accounts for gauge theories with product gauge groups and bifundamental matter. The case of massive orientifold gauge theories with gauge group SO/Sp is also described. In the case with no gravitational corrections the results are shown to be in agreement with Seiberg-Witten analysis and previous results in the literature.

The current experimental lower bound on the Higgs mass significantly restricts the allowed parameter space in most realistic supersymmetric models, with the consequence that these models exhibit significant fine-tuning. We propose a solution to this `supersymmetric little hierarchy problem'. We consider scenarios where the stop masses are relatively heavy - in the 500 GeV to a TeV range. Radiative stability of the Higgs soft mass against quantum corrections from the top quark Yukawa coupling is achieved by imposing a global SU(3) symmetry on this interaction. This global symmetry is only approximate - it is not respected by the gauge interactions. A subgroup of the global symmetry is gauged by the familiar SU(2) of the standard model. The physical Higgs is significantly lighter than the other scalars because it is the pseudo-Goldstone boson associated with the breaking of this symmetry. Radiative corrections to the Higgs potential naturally lead to the right pattern of gauge and global symmetry breaking. We show that both the gauge and global symmetries can be embedded into a single SU(6) grand unifying group, thereby maintaining the prediction of gauge coupling unification. Among the firm predictions of this class of models are new states with the quantum numbers of 10 and under SU(5) close to the TeV scale. The Higgs mass is expected to be below 130 GeV, just as in the MSSM.

Aspects of the supersymmetric extension of the Pohlmeyer invariants are studied, and their relation to superstring boundary states for non-abelian gauge fields is discussed. We show that acting with a super-Pohlmeyer invariant with respect to some non-abelian gauge field A (which has to be constant due to the definition of the Pohlmeyer invariants) on the boundary state of a bare D9 brane produces the boundary state describing that non-abelian background gauge field on the brane if the only non-trivial commutators among the components of A are those involving a single lightlike component. Known consistency conditions on that boundary state equivalent to the background equations of motion for A hence also apply to the quantized Pohlmeyer invariants.

Recently the authors have introduced a new gauged supergravity theory with a positive definite potential in D = 6, obtained through a generalised Kaluza-Klein reduction from D = 7. Of particular interest is the fact that this theory admits certain Minkowski × Sphere vacua. In this paper we extend the previous results by constructing gauged supergravities with positive definitive potentials in diverse dimensions, together with their vacuum solutions. In addition, we prove the supersymmetry of the generalised reduction ansatz. We obtain a supersymmetric solution with no form-field fluxes in the new gauged theory in D = 9. This solution may be lifted to D = 10, where it acquires an interpretation as a time-dependent supersymmetric cosmological solution supported purely by the dilaton. A further uplift to D = 11 yields a solution describing a pp-wave.

= 2 supersymmetric Yang-Mills theories for all classical gauge groups, that is, for SU(N), SO(N), and Sp(N) is considered. The equations which define the Seiberg-Witten curve are proposed. In some cases they are solved. It is shown that for (almost) all models allowed by the asymptotic freedom the 1-instanton corrections which follows from these equations agree with the direct computations and with known results.

The S-matrix Ansatz has been proposed by 't Hooft to overcome difficulties and apparent contradictions of standard quantum field theory close to the black hole horizon. In this paper we revisit and explore some of its aspects. We start by computing gravitational backreaction effects on the properties of the Hawking radiation and explain why a more powerful formalism is needed to encode them. We then use the map bulk-boundary fields to investigate the nature of exchange algebras satisfied by operators associated with ingoing and outgoing matter. We propose and comment on some analogies between the non covariant form of the S-matrix amplitude and liquid droplet physics to end up with similarities with string theory amplitudes via an electrostatic analogy. We finally recall the difficulties that one encounters when trying to incorporate non linear gravity effects in 't Hooft's S-matrix and observe how the inclusion of higher order derivatives might help in the black hole microstate counting.

We construct the most general non-extremal deformation of the D-instanton solution with maximal rotational symmetry. The general non-supersymmetric solution carries electric charges of the SL(2,) symmetry, which correspond to each of the three conjugacy classes of SL(2,). Our calculations naturally generalise to arbitrary dimensions and arbitrary dilaton couplings. We show that for specific values of the dilaton coupling parameter, the non-extremal instanton solutions can be viewed as wormholes of non-extremal Reissner-Nordström black holes in one higher dimension. We extend this result by showing that for other values of the dilaton coupling parameter, the non-extremal instanton solutions can be uplifted to non-extremal non-dilatonic p-branes in p+1 dimensions higher. Finally, we attempt to consider the solutions as instantons of (compactified) type-IIB superstring theory. In particular, we derive an elegant formula for the instanton action. We conjecture that the non-extremal D-instantons can contribute to the R⁸-terms in the type-IIB string effective action.

Finite entropy thermal systems undergo Poincaré recurrences. In the context of field theory, this implies that at finite temperature, timelike two-point functions will be quasi-periodic. In this note we attempt to reproduce this behavior using the AdS/CFT correspondence by studying the correlator of a massive scalar field in the bulk. We evaluate the correlator by summing over all the SL(2,) images of the BTZ spacetime. We show that all the terms in this sum receive large corrections after at certain critical time, and that the result, even if convergent, is not quasi-periodic. We present several arguments indicating that the periodicity will be very difficult to recover without an exact re-summation, and discuss several toy models which illustrate this. Finally, we consider the consequences for the information paradox.

In the string holographic dual of large-N_c QCD with N_f flavours of [1], the η' meson is massless at infinite N_c and dual to a collective fluctuation of N_f D6-brane probes in a supergravity background. Here we identify the string diagrams responsible for the generation of a mass of order N_f/N_c, consistent with the Witten-Veneziano formula, and show that the supergravity limit of these diagrams corresponds to mixings with pseudoscalar glueballs. We argue that the dependence on the θ-angle in the supergravity description occurs only through the combination θ+2(N_f)^1/2 η'/f_π, as dictated by the U(1)_A anomaly. We provide a quantitative test by computing the linear term in the η' potential in two independent ways, with perfect agreement.

In this paper we study the nonperturbative corrections to the generalized Konishi anomaly that come from the strong coupling dynamics of the gauge theory. We consider U(N) gauge theory with adjoint and Sp(N) or SO(N) gauge theory with symmetric or antisymmetric tensor. We study the algebra of chiral rotations of the matter field and show that it does not receive nonperturbative corrections. The algebra implies Wess-Zumino consistency conditions for the generalized Konishi anomaly which are used to show that the anomaly does not receive nonperturbative corrections for superpotentials of degree less than 2l+1 where 2l = 3c(Adj)−c(R) is the one-loop beta function coefficient. The superpotentials of higher degree can be nonperturbatively renormalized because of the ambiguities in the UV completion of the gauge theory. We discuss the implications for the Dijkgraaf-Vafa conjecture.

Many experiments are being planned to measure the neutrino mixing parameter θ₁₃using reactor as well as accelerator neutrino beams. In this note, the theoretical significance of a high precision measurement of this parameter is discussed. It is emphasized that it will provide crucial information about different ways to understand the origin of large atmospheric neutrino mixing and move us closer towards determining the neutrino mass matrix. For instance if exact μ↔τ symmetry in the neutrino mass matrix is assumed to be the reason for maximal ν_μ−ν_τmixing, one gets θ₁₃ = 0. Whether θ₁₃ ≃ (Δm²_⊙/Δm²_A)^1/2 or θ₁₃ ≃ Δm²_⊙/Δm²_Acan provide information about the way the μ↔τ symmetry breaking manifests in the case of normal hierarchy. We also discuss the same question for inverted hierarchy as well as possible gauge theories with this symmetry.

Nonperturbative terms in the free energy of Chern-Simons gauge theory play a key role in its duality to the closed topological string. We show that these terms are reproduced by performing a double scaling limit near the point where the perturbation expansion diverges. This leads to a derivation of closed string theory from this large-N gauge theory along the lines of noncritical string theories. We comment on the possible relevance of this observation to the derivation of superpotentials of asymptotically free gauge theories and its relation to infrared renormalons.

We consider all 1/2 BPS excitations of AdS × S configurations in both type-IIB string theory and M-theory. In the dual field theories these excitations are described by free fermions. Configurations which are dual to arbitrary droplets of free fermions in phase space correspond to smooth geometries with no horizons. In fact, the ten dimensional geometry contains a special two dimensional plane which can be identified with the phase space of the free fermion system. The topology of the resulting geometries depends only on the topology of the collection of droplets on this plane. These solutions also give a very explicit realization of the geometric transitions between branes and fluxes. We also describe all 1/2 BPS excitations of plane wave geometries. The problem of finding the explicit geometries is reduced to solving a Laplace (or Toda) equation with simple boundary conditions. We present a large class of explicit solutions. In addition, we are led to a rather general class of AdS₅ compactifications of M-theory preserving = 2 superconformal symmetry. We also find smooth geometries that correspond to various vacua of the maximally supersymmetric mass-deformed M2 brane theory. Finally, we present a smooth 1/2 BPS solution of seven dimensional gauged supergravity corresponding to a condensate of one of the charged scalars.

We study a model for dynamical localization of topology using ideas from non-commutative geometry and topology in quantum mechanics. We consider a collection X of N one-dimensional manifolds and the corresponding set of boundary conditions (self-adjoint extensions) of the Dirac operator D. The set of boundary conditions encodes the topology and is parameterized by unitary matrices g. A particular geometry is described by a spectral triple x(g) = (A_X,_X,D(g)). We define a partition function for the sum over all g. In this model topology fluctuates but the dimension is kept fixed. We use the spectral principle to obtain an action for the set of boundary conditions. Together with invariance principles the procedure fixes the partition function for fluctuating topologies. The model has one free-parameter β and it is equivalent to a one plaquette gauge theory. We argue that topology becomes localized at β = ∞ for any value of N. Moreover, the system undergoes a third-order phase transition at β = 1 for large-N. We give a topological interpretation of the phase transition by looking how it affects the topology.

We construct the non-extreme solutions of non-orthogonal intersecting D-branes. The solutions reduce to non-extreme black holes upon the toroidal compactification. We clarify the relation between two configurations with equal mass and charge, one of which is non-orthogonal intersecting D-branes and the other one is orthogonal D-branes, from supergravity and string theory perspective. We also calculate mass and entropies for these black holes.

In this note we demonstrate that chaotic inflation can naturally be realized in the context of an anomaly free minimal gauged supergravity in D = 6 which has recently been the focus of some attention. This particular model has a unique maximally symmetric ground state solution, R^3,1 × S² which leaves half of the six-dimensional supersymmetries unbroken. In this model, the inflaton field ϕ originates from the complex scalar fields in the D = 6 scalar hyper-multiplet. The mass and the self couplings of the scalar field are dictated by the D = 6 lagrangian. The scalar potential has an absolute minimum at ϕ = 0 with no undetermined moduli fields. Imposing a mild bound on the radius of S² enables us to obtain chaotic inflation. The low energy equations of motion are shown to be consistent for the range of scalar field values relevant for inflation.

In the Green-Schwarz formalism, the closed string worldsheet of the IIB theory couples to Ramond-Ramond (RR) fluxes through spinor bilinears. We study the effect of such fluxes by analyzing the supersymmetry transformation of the worldsheet in general backgrounds. We show that, in the presence RR fields, the closed string can get `polarized', as the spinors acquire non-zero vevs in directions correlating with the orientation of close-by D-branes. Reversing the argument, this may allow for worldsheet configurations—with non-trivial spinor structure—that source RR moments.

We study both the classical and the quantum target space of (p,q) minimal string theory, using the FZZT brane as a probe. By thinking of the target space as the moduli space of FZZT branes, parametrized by the boundary cosmological constant x, we see that classically it consists of a Riemann surface _p,q which is a p-sheeted cover of the complex x plane. However, we show using the dual matrix model that the exact quantum FZZT observables exhibit Stokes' phenomenon and are entire functions of x. Along the way we clarify some points about the semiclassical limit of D-brane correlation functions. The upshot is that nonperturbative effects modify the target space drastically, changing it from _p,q to the complex x plane. To illustrate these ideas, we study in detail the example of (p,q) = (2,1), which is dual to the gaussian matrix model. Here we learn that the other sheets of the classical Riemann surface describe instantons in the effective theory on the brane. Finally, we discuss possible applications to black holes and the topological string.

The equations of 10 or 11 dimensional supergravity admit supersymmetric compactifications on 7-manifolds of G₂ holonomy, but these supergravity vacua are deformed away from special holonomy by the higher-order corrections of string or M-theory. We find simple expressions for the first-order corrections to the Einstein and Killing spinor equations in terms of the calibrating 3-form of the leading-order G₂-holonomy background. We thus obtain, and solve explicitly, systems of first-order equations describing the corrected metrics for most of the known classes of cohomogeneity-one 7-metrics with G₂ structures.

The current cosmic acceleration does not imply that our Universe is basically de Sitter-like: in the first part of this work we argue that, by introducing matter into anti-de Sitter spacetime in a natural way, one may be able to account for the acceleration just as well. However, this leads to a Big Crunch, and the euclidean versions of Bang/Crunch cosmologies have [apparently] disconnected conformal boundaries. As Maldacena and Maoz have recently stressed, this seems to contradict the holographic principle. In the second part we argue that this ``double boundary problem" is a matter not of geometry but rather of how one chooses a conformal compactification: if one chooses to compactify in an unorthodox way, then the appearance of disconnectedness can be regarded as a coordinate effect. With the kind of matter we have introduced here, namely a euclidean axion, the underlying compact euclidean manifold has an unexpectedly non-trivial topology: it is in fact one of the 75 possible underlying manifolds of flat compact four-dimensional euclidean spaces.

We study the process of tachyonic preheating using approximative quantum equations of motion derived from the 2PI effective action. The O(N) scalar (Higgs) field is assumed to experience a fast quench which is represented by an instantaneous flip of the sign of the mass parameter. The equations of motion are solved numerically on the lattice, and the Hartree and 1/N-NLO approximations are compared to the classical approximation. Classical dynamics is expected to be valid, since the occupation numbers can rise to large values during tachyonic preheating. We find that the classical approximation performs excellently at short and intermediate times, even for couplings in the larger region currently allowed for the SM Higgs. This is reassuring, since all previous numerical studies of tachyonic preheating and baryogenesis during tachyonic preheating have used classical dynamics. We also compare different initializations for the classical simulations.

We propose Bethe equations for the diagonalization of the hamiltonian of quantum strings on AdS₅ × S⁵at large string tension and restricted to certain large charge states from a closed (2) subsector. The ansatz differs from the recently proposed all-loop gauge theory asymptotic Bethe ansatz by additional factorized scattering terms for the local excitations. We also show that our ansatz quantitatively reproduces everything that is currently known about the string spectrum of these states. Firstly, by construction, we recover the integral Bethe equations describing semiclassical spinning strings. Secondly, we explain how to derive the 1/J energy corrections of M-impurity BMN states, provide explicit, general formulae for both distinct and confluent mode numbers, and compare to asymptotic gauge theory. In the special cases M = 2,3 we reproduce the results of direct quantization of Callan et al. Lastly, at large string tension and relatively small charge we recover the famous 2(n²λ)^1/4 asymptotics of massive string modes at level n. Remarkably, this behavior is entirely determined by the novel scattering terms. This is qualitatively consistent with the conjecture that these terms occur due to wrapping effects in gauge theory. Our finding does not in itself cure the disagreements between gauge and string theory, but leads us to speculate about the structure of an interpolating Bethe ansatz for the AdS/CFT system at finite coupling and charge.

We analyse the direct detection of neutralino dark matter in supergravity scenarios with non-universal soft scalar and gaugino masses. In particular, the neutralino-nucleon cross section is computed and compared with the sensitivity of detectors. We take into account the most recent experimental and astrophysical constraints on the parameter space, including those coming from charge and colour breaking minima. Gaugino non-universalities provide a larger flexibility in the neutralino sector. In particular, when combined with non-universal scalars, neutralinos close to the present detection limits are possible with a wide range of masses, from over 400 GeV to almost 10 GeV. We study the different possibilities which allow to increase or decrease the neutralino mass and explain the properties of those regions in the parameter space with a large cross section.

We have performed a detailed Monte Carlo exploration of the parameter space for a warped Higgsless model of electroweak symmetry breaking in 5 dimensions. This model is based on the SU(2)_L × SU(2)_R × U(1)_B−L gauge group in an AdS₅ bulk with arbitrary gauge kinetic terms on both the Planck and TeV branes. Constraints arising from precision electroweak measurements and collider data are found to be relatively easy to satisfy. We show, however, that the additional requirement of perturbative unitarity up to the cut-off, ≃ 10 TeV, in W_L⁺W_L⁻ elastic scattering in the absence of dangerous tachyons eliminates all models. If successful models of this class exist, they must be highly fine-tuned.

We provide a systematic and practical method of deriving 5D supergravity action described by 4D superfields on a general warped geometry, including a non-BPS background. Our method is based on the superconformal formulation of 5D supergravity, but is easy to handle thanks to the superfield formalism. We identify the radion superfield in the language of 5D superconformal gravity, and clarify its appearance in the action. We also discuss SUSY breaking effects induced by a deformed geometry due to the backreaction of the radius stabilizer.

We present new M2 and M5 brane solutions in M-theory based on transverse Atiyah-Hitchin space and other self-dual geometries. One novel feature of these solutions is that they have bolt-like fixed points yet still preserve 1/4 of the supersymmetry. All the solutions can be reduced down to ten dimensional intersecting brane configurations.

We generalize the work of Deser and Levin on the unified description of Hawking radiation and Unruh effect to general stationary motions in spherically symmetric black holes. We have also matched the chemical potential term of the thermal spectrum of the two sides for uncharged black holes.

It is well known that technicolor models in which the electroweak symmetry is broken by QCD-like strong dynamics at the TeV scale generally predict unacceptably large corrections to low-energy observables. We investigate the models of electroweak symmetry breaking by strong dynamics in which the gauge symmetry is extended to include an arbitrary number of additional SU(2) and U(1) factors. This class of models includes the deconstructed version of the recently proposed five-dimensional ``Higgsless'' scenario. We conclude that the additional structure present in these theories does not suppress the effects of strongly coupled short-distance physics on the precision electroweak observables. In particular, the possibility that the symmetry breaking is due to QCD-like dynamics is still strongly disfavored by data.

In this paper we show how S-duality of type-IIB superstrings leads to an S-duality relating A- and B-model topological strings on the same Calabi-Yau as had been conjectured recently: D-instantons of the B-model correspond to A-model perturbative amplitudes and D-instantons of the A-model capture perturbative B-model amplitudes. Moreover this confirms the existence of new branes in the two models. As an application we explain the recent results concerning A-model topological strings on Calabi-Yau and its equivalence to the statistical mechanical model of melting crystal.

We study the properties of a D-brane in the presence of k NS5 branes. The Dirac-Born-Infeld action describing the dynamics of this D-brane is very similar to that of a non-BPS D-brane in ten dimensions. As the D-brane approaches the fivebranes, its equation of state approaches that of a pressureless fluid. In non-BPS D-brane case this is considered as an evidence for the decay of the D-brane into ``tachyon matter''. We show that in our case similar behavior is the consequence of the motion of the D-brane. In particular in the rest frame of the moving D-brane the equation of state is that of a usual D-brane, for which the pressure is equal to the energy density. We also compute the total cross-section for the decay of the D-brane into closed string modes and show that the emitted energy has a power like divergence for D0, D1 and D2 branes, while converges for higher dimensional D-branes. We also speculate on the possibility that the infalling D-brane describes a decaying defect in six dimensional Little String Theory.

We obtain the entropy of Schwarzschild and charged black holes in D > 4 from superconformal gases that live on p = 10−D dimensional brane-antibrane systems wrapped on T^p. The properties of strongly coupled superconformal theories such as the appearance of hidden dimensions (for p = 1,4) and fractional strings (for p = 5) are crucial for our results. In all cases, the Schwarzschild radius is given by the transverse fluctuations of the branes and antibranes due to the finite temperature. We show that our results can be generalized to multicharged black holes.

We show how the superembedding formalism can be applied to construct manifestly kappa-symmetric higher derivative corrections for the D9-brane. We also show that all correction terms appear at even powers of the fundamental length scale l. We explicitly construct the first potential correction, which corresponds to the kappa-symmetric version of the ∂⁴F⁴, which one finds from the four-point amplitude of the open superstring.

We report on a very accurate measurement of the static quark potential in SU(2) Yang-Mills theory in (2+1) dimensions in order to study the corrections to the linear behaviour. We perform numerical simulations at zero and finite temperature comparing our results with the corrections given by the effective string picture in these two regimes. We also check for universal features discussing our results together with those recently published for the (2+1)-d (2) and SU(3) pure gauge theories.

We elaborate on the relations between surface states and squeezed states. First, we investigate two different criteria for determining whether a matter sector squeezed state is also a surface state and show that the two criteria are equivalent. Then, we derive similar criteria for the ghost sector. Next, we refine the criterion for determining whether a surface state is in _κ², the subalgebra of squeezed states obeying [S,K₁²] = 0. This enables us to find all the surface states of the _κ² subalgebra, and show that it consists only of wedge states and (hybrid) butterflies. Finally, we investigate generalizations of this criterion and find an infinite family of surface states subalgebras, whose surfaces are described using a ``generalized Schwarz-Christoffel'' mapping.

The electromagnetic form factors of the proton are obtained using a particular realization of QCD in the large N_c limit (QCD_∞), which sums up the infinite number of zero-width resonances to yield an Euler's Beta function (Dual-QCD_∞). The form factors F₁(q²) and F₂(q²), as well as G_M(q²) agree very well with reanalyzed space-like data in the whole range of momentum transfer. In addition, the predicted ratio μ_pG_E/G_M is in good agreement with recent polarization transfer measurements at Jefferson Lab.

It was suggested by A. Kapustin that turning on a B-field, and allowing some discrepancy between the left and and right-moving complex structures, must induce an identification of B-branes with holomorphic line bundles on a non-commutative complex torus. The stability condition for the branes is written as a topological identity of non-commutative gauge theory. This identifies stable B-branes with previously proposed non-commutative instanton equations. Consistency of the non-commutative description with complex geometry is examined, using the non-linearities of the Seiberg-Witten map.

We show that requiring sixteen supersymmetries in quantum mechanical gauge theory implies the existence of a web of constrained interactions. Contrary to conventional wisdom, these constraints extend to arbitrary orders in the momentum expansion.