Table of contents

We evaluate the spectral function of scalar and spinor propagator in three dimensional quantum electrodynamics with the use of Ward-Identity for soft-photon emission vertex. Exponentation of one-photon matrix element yields a full propagator in position space. It has asimple form as free propagator multiplied by quantum correction. But this is not an integrable function so that analysis in momentum space is not easy. Term by term integral converges and they have a logarithmic singularity associated with renormalized mass in perturbation theory. Renormalization constant vanishes for weak coupling,which suggests confinement of charged particle. There exsists a critical coupling constant below which bare mass vanishes and the vacuum expectation value of pair condensation is finite.

Fermionic extensions of generic 2d gravity theories obtained from the graded Poisson-Sigma model (gPSM) approach show a large degree of ambiguity. In addition, obstructions may reduce the allowed range of fields as given by the bosonic theory, or even prohibit any extension in certain cases. In our present work we relate the finite W-algebras inherent in the gPSM algebra of constraints to algebras which can be interpreted as supergravities in the usual sense (Neuveu-Schwarz or Ramond algebras resp.), deformed by the presence of the dilaton field. With very straightforward and natural assumptions on them — like demanding rigid supersymmetry in a certain flat limit, or linking the anti-commutator of certain fermionic charges to the hamiltonian constraint — in the ``genuine'' supergravity obtained in this way the ambiguities disappear, as well as the obstructions referred to above. Thus all especially interesting bosonic models (spherically reduced gravity, the Jackiw-Teitelboim model etc.) under these conditions possess a unique fermionic extension and are free from new singularities. The superspace supergravity model of Howe is found as a special case of this supergravity action. For this class of models the relation between bosonic potential and prepotential does not introduce obstructions as well.

N = 1 and 2 superconformal boundary conditions are shown to be the consequence of a ``boundary'' on the worldsheet superspace with positive codimension in the anticommuting subspace. In addition to the well-known boundary conditions, I also find two new infinite series of N = 2 boundary states. Their free field realizations are given. A self-contained development of 2d superspace leads to new perspectives on this subject.

We find a nonsupersymmetric dilatonic deformation of AdS₅ geometry as an exact nonsingular solution of the type-IIB supergravity. The dual gauge theory has a different Yang-Mills coupling in each of the two halves of the boundary spacetime divided by a codimension one defect. We discuss the geometry of our solution in detail, emphasizing the structure of the boundary, and also study the string configurations corresponding to Wilson loops. We also show that the background is stable under small scalar perturbations.

Moduli spaces of conformal field theories corresponding to current-current deformations are discussed. For WZW models, CFT and sigma model considerations are compared. It is shown that current-current deformed WZW models have WZW-like sigma model descriptions with non-bi-invariant metrics, additional B-fields and a non-trivial dilaton.

We consider the geometrical description of N = 8 supergravity in central charge superspace and present in detail the deduction from this geometrical formulation of both the supergravity transformations and the equations of motion for the component fields. We compare these results with those already known and obtained in formulations on the component level.

This is a note on the coupled supergravity-tachyon matter system, which has been earlier proposed as a candidate for the effective space-time description of S-branes. In particular, we study an ansatz with the maximal ISO(p+1) × SO(8−p,1) symmetry, for general brane dimensionality p and homogeneous brane distribution in transverse space ρ_⊥. A simple application of singularity theorems shows that (for p ⩽ 7) the most general solution with these symmetries is always singular. (This invalidates a recent claim in the literature.) We include a few general comments about the possibility of describing the decay of unstable D-branes in purely gravitational terms.

Gauge theories in 2+1 dimensions whose gauge symmetry is spontaneously broken to a finite group enjoy a quantum group symmetry which includes the residual gauge symmetry. This symmetry provides a framework in which fundamental excitations (electric charges) and topological excitations (magnetic fluxes) can be treated on an equal footing. In order to study symmetry breaking by both electric and magnetic condensates we develop a theory of symmetry breaking which is applicable to models whose symmetry is described by a quantum group (quasitriangular Hopf algebra). Using this general framework we investigate the symmetry breaking and confinement phenomena which occur in (2+1)-dimensional gauge theories. Confinement of particles is linked to the formation of string-like defects. Symmetry breaking by an electric condensate leads to magnetic confinement and vice-versa. We illustrate the general formalism with examples where the symmetry is broken by electric, magnetic and dyonic condensates.

Gravitinos with a mass in the keV range are an interesting candidate for warm dark matter. Recent measurements of the matter density of the universe and of cosmic structures at the dwarf galaxy scale rule out the simplest gravitino models with thermal freeze-out. We construct a model where the decay of the messenger particles that transmit the supersymmetry breaking to the observable sector generates the required entropy to dilute the gravitino relic density by the required factor of a few to come in line with observations. The model is natural, and requires only that the coupling of the messenger sector to the standard model be set so that the decay happens at the appropriate time.

We use the matrix model — gauge theory correspondence of Dijkgraaf and Vafa in order to construct the geometry encoding the exact gaugino condensate superpotential for the = 1 U(N) gauge theory with adjoint and symmetric or anti-symmetric matter, broken by a tree level superpotential to a product subgroup involving U(N_i) and SO(N_i) or Sp(N_i/2) factors. The relevant geometry is encoded by a non-hyperelliptic Riemann surface, which we extract from the exact loop equations. We also show that O(1/N) corrections can be extracted from a logarithmic deformation of this surface. The loop equations contain explicitly subleading terms of order 1/N, which encode information of string theory on an orientifolded local quiver geometry.

We study the dipole moments, electric dipole moment, weak electric dipole moment, anomalous magnetic moment, anomalous weak magnetic moment, of fermions in the noncommutative extension of the SM. We observe that the noncommutative effects are among the possible candidates to explain the electric and weak electric dipole moment of fermions. Furthermore, the upper bounds for the parameters which carry space-time and space-space noncommutativity can be obtained by using the theoretical and experimental results of the fermion dipole moments.

We study four dimensional = 2 SO/SP supersymmetric gauge theory on R³ × S¹ deformed by a tree level superpotential. We will show that the exact superpotential can be obtained by making use of the Lax matrix of the corresponding integrable model which is the periodic Toda lattice. The connection between vacua of SO(2N) and SO(2kN−2k+2) can also be seen in this framework. Similar analysis can also be applied for SO(2N+1) and SP(2N).

We study the = 1 version of Argyres-Douglas (AD) points by making use of the recent developments in understanding the dynamics of the chiral sector of = 1 gauge theories. We shall consider = 1 U(N) gauge theories with an adjoint matter and look for the tree-level superpotential W(x) which reproduces the = 2 AD points via the factorization equation relating the = 1 and = 2 curves. We find that the following superpotentials generate the = 2 AD points: (1) W'(x) = x^N±2Λ^N, (2) W'(x) = xⁿ,N−1 ⩾ n ⩾ N/2+1. In case (1) the physics is essentially the same as the = 2 theory even in the presence of the superpotential. There seems to be an underlying structure of N-reduced KP hierarchy in the system. Case (2) occurs at the intersection of a number of = 1 vacua with massless monopoles. This branch of vacua is characterized by having s₊ = 0 or s₋ = 0 where s_±denotes the number of double roots in P_N(x)±2Λ^N. It is possible to show that the mass gap in fact vanishes at this AD point. We conjecture that it represents a new class of = 1 superconformal field theory.

We propose a useful method for deriving the effective theory for a system where BPS and anti-BPS domain walls coexist. Our method respects an approximately preserved SUSY near each wall. Due to the finite width of the walls, SUSY breaking terms arise at tree-level, which are exponentially suppressed. A practical approximation using the BPS wall solutions is also discussed. We show that a tachyonic mode appears in the matter sector if the corresponding mode function has a broader profile than the wall width.

By applying mirror symmetry to D-branes in a Calabi-Yau geometry we shed light on a G₂ flop in M-theory relevant for large N dualities in = 1 supersymmetric gauge theories. Furthermore, we derive superpotential for M-theory on corresponding G₂ manifolds for all A-D-E cases. This provides an effective method for geometric engineering of = 1 gauge theories for which mirror symmetry gives exact information about vacuum geometry. We also find a number of interesting dual descriptions.

We show that a large class of supersymmetric compactifications, including all simply connected Calabi-Yau and G₂ manifolds, have classical configurations with negative energy density as seen from four dimensions. In fact, the energy density can be arbitrarily negative - it is unbounded from below. Nevertheless, positive energy theorems show that the total ADM energy remains positive. Physical consequences of the negative energy density include new thermal instabilities, and possible violations of cosmic censorship.

We derive the Konishi anomaly equations for = 1 supersymmetric gauge theories based on the classical gauge groups with matter in two-index tensor and fundamental representations, thus extending the existing results for U(N). A general formula is obtained which expresses solutions to the Konishi anomaly equation in terms of solutions to the loop equations of the corresponding matrix model. This provides an alternative to the diagrammatic proof that the perturbative part of the glueball superpotential W_eff for these matter representations can be computed from matrix model integrals, and further shows that the two approaches always give the same result. The anomaly approach is found to be computationally more efficient in the cases we studied. Also, we show in the anomaly approach how theories with a traceless two-index tensor can be solved using an associated theory with a traceful tensor and appropriately chosen coupling constants.

We show that the scattering amplitude of four open string scalars or tachyons on the world-volume of a Dp-brane in the bosonic string theory can be written in a universal form. The difference between this amplitude and the corresponding amplitude in the superstring theory is in an extra tachyonic pole. We show that in an α' expansion and for slowly varying fields, the amplitude is consistent with the tachyonic DBI action in which the even part of the tachyon potential is V(T) = e^{−((π)1/2T/α)2} with α = 1 for bosonic theory and α = (2)^1/2 for superstring theory.

A simple extension of the minimal supersymmetric standard model which naturally and simultaneously solves the strong CP and μ problems via a Peccei-Quinn and a continuous R symmetry is considered. This model is supplemented with hybrid inflation and leptogenesis, but without taking the specific details of these scenarios. It is shown that the Peccei-Quinn field can successfully act as a curvaton generating the total curvature perturbation in the universe in accord with the cosmic background explorer measurements. A crucial phenomenon, which assists us to achieve this, is the `tachyonic amplification' of the perturbation acquired by this field during inflation if the field, in its subsequent evolution, happens to be stabilized for a while near a maximum of the potential. In this case, the contribution of the field to the total energy density is also enhanced (`tachyonic effect'), which helps too. The cold dark matter in the universe consists, in this model, mainly of axions which carry an isocurvature perturbation uncorrelated with the total curvature perturbation. There are also lightest sparticles (neutralinos) which, like the baryons, originate from the inflationary reheating and, thus, acquire an isocurvature perturbation fully correlated with the curvature perturbation. So, the overall isocurvature perturbation has a mixed correlation with the adiabatic one. It is shown that the presently available bound on such an isocurvature perturbation from cosmic microwave background radiation and other data is satisfied. Also, the constraint on the non-gaussianity of the curvature perturbation obtained from the recent Wilkinson microwave anisotropy probe data is fulfilled thanks to the `tachyonic effect'.

It is shown that the four-particle amplitude of superstring theory at two loops obtained in [1], [2] is equivalent to the previously obtained results in [3]-[5]. Here the ₂ symmetry in hyperelliptic Riemann surface plays an important role in the proof.

We study aspects of the interaction between a D-brane and an anti-D-brane in the maximally supersymmetric plane wave background of type IIB superstring theory, which is equipped with a mass parameter μ. An early such study in flat spacetime (μ = 0) served to sharpen intuition about D-brane interactions, showing in particular the key role of the ``stringy halo'' that surrounds a D-brane. The halo marks the edge of the region within which tachyon condensation occurs, opening a gateway to new non-trivial vacua of the theory. It seems pertinent to study the fate of the halo for non-zero μ. We focus on the simplest cases of a lorentzian brane with p = 1 and an euclidean brane with p = −1, the D-instanton. For the lorentzian brane, we observe that the halo is unaffected by the presence of non-zero μ. This most likely extends to other (lorentzian) p. For the euclidean brane, we find that the halo is affected by non-zero μ. As this is related to subtleties in defining the exchange amplitude between euclidean branes in the open string sector, we expect this to extend to all euclidean branes in this background.

We present a systematic derivation of multi-instanton amplitudes in terms of ADHM equivariant cohomology. The results rely on a supersymmetric formulation of the localization formula for equivariant forms. We examine the cases of = 4 and = 2 gauge theories with adjoint and fundamental matter.

In a wide class of new-physics models, which can be motivated through generic arguments and within supersymmetry, we obtain large contributions to B⁰_d–⁰_d mixing, but not to ΔB = 1 processes. If we assume such a scenario, the solutions ϕ_d ∼ 47^o V 133^o for the B⁰_d–⁰_d mixing phase implied by _CP^mix(B_d→J/ψK_S) cannot be converted directly into a constraint in the – plane. However, we may complement ϕ_dwith |V_ub/V_cb| and the recently measured CP asymmetries in B_d→π⁺π⁻to determine the unitarity triangle, with its angles α, β and γ. To this end, we have also to control penguin effects, which we do by means of the CP-averaged B_d→π^∓K^±branching ratio. Interestingly, the present data show a perfectly consistent picture not only for the ``standard'' solution of ϕ_d ∼ 47^o, but also for ϕ_d ∼ 133^o. In the latter case, the preferred region for the apex of the unitarity triangle is in the second quadrant, allowing us to accommodate conveniently γ>90^o, which is also favoured by other non-leptonic B decays such as B→πK. Moreover, also the prediction for BR(K⁺→π⁺ν) can be brought to better agreement with experiment. Further strategies to explore this scenario with the help of B_d,s→μ⁺μ⁻decays are discussed as well.

A numerical simulation algorithm for lattice QCD is described, in which the short- and long-distance effects of the sea quarks are treated separately. The algorithm can be regarded, to some extent, as an implementation at the quantum level of the classical Schwarz alternating procedure for the solution of elliptic partial differential equations. No numerical tests are reported here, but theoretical arguments suggest that the algorithm should work well also at small quark masses.

Results are presented of a full leading-order evaluation of the shear viscosity, flavor diffusion constants, and electrical conductivity in high temperature QCD and QED. The presence of Coulomb logarithms associated with gauge interactions imply that the leading-order results for transport coefficients may themselves be expanded in an infinite series in powers of 1/log (1/g); the utility of this expansion is also examined. A next-to-leading-log approximation is found to approximate the full leading-order result quite well as long as the Debye mass is less than the temperature.

We review the most general, local, superconformal boundary conditions for the two-dimensional N = 1 and N = 2 non-linear sigma models, and analyse them for the N = 1 and N = 2 supersymmetric WZW models. We find that the gluing map between the left and right affine currents is generalised in a very specific way as compared to the constant Lie algebra automorphisms that are known.

We investigate supersymmetric QCD with N_c+1 flavors using an extension of the recently proposed relation between gauge theories and matrix models. The impressive agreement between the two sides provides a beautiful confirmation of the extension of the gauge theory-matrix model relation to this case.

Diaconescu, Moore and Witten have shown that the topological part of the M-theory partition function is an invariant of an E₈ gauge bundle over the 11-dimensional bulk. Any construction of 11d SUGRA from gauge bundle data must satisfy a number of constraints in order to correctly reproduce the the known 10-dimensional physics on each boundary component. We analyse these constraints and in particular use them to attempt an approximate construction of the 11d gravitino as a condensate of the gauge theory fields.

We compute the billiards that emerge in the Belinskii-Khalatnikov-Lifshitz (BKL) limit for all pure supergravities in D = 4 spacetime dimensions, as well as for D = 4, N = 4 supergravities coupled to k (N = 4) Maxwell supermultiplets. We find that just as for the cases N = 0 and N = 8 investigated previously, these billiards can be identified with the fundamental Weyl chambers of hyperbolic Kac-Moody algebras. Hence, the dynamics is chaotic in the BKL limit. A new feature arises, however, which is that the relevant Kac-Moody algebra can be the lorentzian extension of a twisted affine Kac-Moody algebra, while the N = 0 and N = 8 cases are untwisted. This occurs for N = 5, where one gets A₄^(2)∧, and for N = 3 and 2, for which one gets A₂^(2)∧. An understanding of this property is provided by showing that the data relevant for determining the billiards are the restricted root system and the maximal split subalgebra of the finite-dimensional real symmetry algebra characterizing the toroidal reduction to D = 3 spacetime dimensions. To summarise: split symmetry controls chaos.

We discuss systematic approaches to the classification of string/M theory vacua, and physical questions this might help us resolve. To this end, we initiate the study of ensembles of effective lagrangians, which can be used to precisely study the predictive power of string theory, and in simple examples can lead to universality results. Using these ideas, we outline an approach to estimating the number of vacua of string/M theory which can realize the Standard Model.

Compactifying a higher-dimensional theory defined in ^1,3+n on an n-dimensional manifold results in a spectrum of four-dimensional (bosonic) fields with masses m²_i = λ_i, where −λ_i are the eigenvalues of the laplacian on the compact manifold. The question we address in this paper is the inverse: given the masses of the Kaluza-Klein fields in four dimensions, what can we say about the size and shape (i.e. the topology and the metric) of the compact manifold? We present some examples of isospectral manifolds (i.e., different manifolds which give rise to the same Kaluza-Klein mass spectrum). Some of these examples are Ricci-flat, complex and Kähler and so they are isospectral backgrounds for string theory. Utilizing results from finite spectral geometry, we also discuss the accuracy of reconstructing the properties of the compact manifold (e.g., its dimension, volume, and curvature etc) from measuring the masses of only a finite number of Kaluza-Klein modes.

This is a study of holomorphic matrix models, the matrix models which underlie the conjecture of Dijkgraaf and Vafa. I first give a systematic description of the holomorphic one-matrix model. After discussing its convergence sectors, I show that certain puzzles related to its perturbative expansion admit a simple resolution in the holomorphic set-up. Constructing a `complex' microcanonical ensemble, I check that the basic requirements of the conjecture (in particular, the special geometry relations involving chemical potentials) hold in the absence of the hermiticity constraint. I also show that planar solutions of the holomorphic model probe the entire moduli space of the associated algebraic curve. Finally, I give a brief discussion of holomorphic ADE models, focusing on the example of the A<sub>2</sub> quiver, for which I extract explicitly the relevant Riemann surface. In this case, use of the holomorphic model is crucial, since the hermitean approach and its attending regularization would lead to a singular algebraic curve, thus contradicting the requirements of the conjecture. In particular, I show how an appropriate regularization of the holomorphic A<sub>2</sub> model produces the desired smooth Riemann surface in the limit when the regulator is removed, and that this limit can be described as a statistical ensemble of `reduced' holomorphic models.

We study time dependent solutions in cubic open string field theory which are expected to describe the configuration of the rolling tachyon. We consider the truncated system consisting of component fields of level zero and two, which are expanded in terms of cosh nx⁰ modes. For studying the large time behavior of the solution we need to know the coefficients of all and, in particular, large n modes. We examine numerically the coefficients of the n-th mode, and find that it has the leading n-dependence of the form (−β)ⁿ λ⁻ⁿ² multiplied by a peculiar subleading part with peaks at n = 2^m = 4,8,16,32,64,128,.... This behavior is also reproduced analytically by solving simplified equations of motion of the tachyon system.

The axial anomaly arising from the fermion sector of U(N) or SU(N) reduced model is studied under a certain restriction of gauge field configurations (the ``U(1) embedding'' with N = L^d). We use the overlap-Dirac operator and consider how the anomaly changes as a function of a gauge-group representation of the fermion. A simple argument shows that the anomaly vanishes for an irreducible representation expressed by a Young tableau whose number of boxes is a multiple of L² (such as the adjoint representation) and for a tensor-product of them. We also evaluate the anomaly for general gauge-group representations in the large N limit. The large N limit exhibits expected algebraic properties as the axial anomaly. Nevertheless, when the gauge group is SU(N), it does not have a structure such as the trace of a product of traceless gauge-group generators which is expected from the corresponding gauge field theory.

We use Ward identities derived from the generalized Konishi anomaly in order to compute effective superpotentials for SU(N), SO(N) and Sp(N) supersymmetric gauge theories coupled to matter in various representations. In particular we focus on cubic and quartic tree level superpotentials. With this technique higher order corrections to the perturbative part of the effective superpotential can be easily evaluated.

We construct smooth Calabi-Yau threefolds Z, torus-fibered over a dP₉ base, with fundamental group π₁ = ₂ × ₂. To do this, the structure of rational elliptic surfaces is studied and it is shown that a restricted subset of such surfaces admit at least a ₂ × ₂ group of automorphisms. One then constructs Calabi-Yau threefolds X as the fiber product of two such dP₉ surfaces, demonstrating that the involutions on the surfaces lift to a freely acting ₂ × ₂ group of automorphisms on X. The threefolds Z are then obtained as the quotient Z = X/(₂ × ₂). These Calabi-Yau spaces Z admit stable, holomorphic SU(4) vector bundles which, in conjunction with ₂ × ₂ Wilson lines, lead to standard-like models of particle physics with naturally suppressed nucleon decay.

We consider Penrose limits of the Klebanov-Strassler and Maldacena-Núñez holographic duals to = 1 supersymmetric Yang-Mills. By focusing in on the IR region we obtain exactly solvable string theory models. These represent the nonrelativistic motion and low-lying excitations of heavy hadrons with mass proportional to a large global charge. We argue that these hadrons, both physically and mathematically, take the form of heavy nonrelativistic strings; we term them ``annulons.'' A simple toy model of a string boosted along a compact circle allows us considerable insight into their properties. We also calculate the Wilson loop carrying large global charge and show the effect of confinement is quadratic, not linear, in the string tension.

It is known that certain theories with extended supersymmetry can be discretized in such a way as to preserve an exact fermionic symmetry. In the simplest model of this kind, we show that this residual supersymmetric invariance is actually a BRST symmetry associated with gauge fixing an underlying local shift symmetry. Furthermore, the original lattice action is then seen to be entirely a gauge fixing term. The corresponding continuum theory has a topological field theory interpretation. We look, in detail, at one example - supersymmetric quantum mechanics which possesses two such BRST symmetries. In this case, we show that the lattice theory can be obtained by blocking out of the continuum in a carefully chosen background metric. Such a procedure will not change the Ward identities corresponding to the BRST symmetries since they correspond to topological observables. Thus, at the quantum level, the continuum BRST symmetry is preserved in the lattice theory. Similar conclusions are reached for the two-dimensional complex Wess-Zumino model and imply that all the supersymmetric Ward identities are satisfied exactly on the lattice. Numerical results supporting these conclusions are presented.

We construct a variety of supersymmetric gauge theories on a spatial lattice, including N = 4 supersymmetric Yang-Mills theory in 3+1 dimensions. Exact lattice supersymmetry greatly reduces or eliminates the need for fine tuning to arrive at the desired continuum limit in these examples.

A Higgs boson with richer flavor interactions arises when the flavor structure encoded in supersymmetric extensions of the standard model is transmitted to the Higgs sector. The flavor-Higgs transmission mechanism can have a radiative or mixing origin, as it is illustrated with several examples, and can produce interesting Higgs signatures that can be probed at future high-energy colliders. Within the minimal SUSY extension of the SM (MSSM), the flavor mediation mechanism is of radiative type, as it is realized through gaugino-sfermion loops, and it transmits the flavor structure of the soft-breaking sector to the Higgs bosons; for this case we evaluate the contributions from general trilinear A-terms to the Lepton Flavor-Violating (LFV) and Flavor-Conserving (LFC) Higgs vertices. On the other hand, as an example of flavor mediation through mixing, we discuss an E₆-inspired multi-Higgs model, supplemented with an abelian flavor symmetry, where LFV as well as LFC Higgs effects, are found to arise, though in this case at tree-level. We find that Tevatron and LHC can provide information on the flavor structure of these models through the detection of the LFV Higgs mode h→τμ, while NLC can perform high-precision tests of the LFC mode h→τ⁺τ⁻.

Electromagnetic plane waves provide examples of time-dependent open string backgrounds free of α' corrections. The solvable case of open strings in a quadrupolar wave front, analogous to pp-waves for closed strings, is discussed. In light-cone gauge, it leads to non-conformal boundary conditions similar to those induced by tachyon condensates. A maximum electric gradient is found, at which macroscopic strings with vanishing tension are pair-produced — a non-relativistic analogue of the Born-Infeld critical electric field. Kinetic instabilities of quadrupolar electric fields are cured by standard atomic physics techniques, and do not interfere with the former dynamic instability. A new example of non-conformal open-closed duality is found. Propagation of open strings in time-dependent wave fronts is discussed.

We introduce a computational technique for studying non-supersymmetric deformations of domain wall solutions of interest in AdS/CFT. We focus on the Klebanov-Strassler solution, which is dual to a confining gauge theory. From an analysis of asymptotics we find that there are three non-supersymmetric deformations that leave the ten-dimensional supergravity solution regular and preserve the global bosonic symmetries of the supersymmetric solution. Also, we show that there are no regular near-extremal deformations preserving the global symmetries, as one might expect from the existence of a gap in the gauge theory.

We study the large-N limit of the class of U(N) = 1 SUSY gauge theories with an adjoint scalar and a superpotential W(Φ). In each of the vacua of the quantum theory, the expectation values <TrΦ^p> are determined by a master matrix Φ₀ with eigenvalue distribution ρ_GT(λ). ρ_GT(λ) is quite distinct from the eigenvalue distribution ρ_MM(λ) of the corresponding large-N matrix model proposed by Dijkgraaf and Vafa. Nevertheless, it has a simple form on the auxiliary riemann surface of the matrix model. Thus the underlying geometry of the matrix model leads to a definite prescription for computing ρ_GT(λ), knowing ρ_MM(λ).

We extend the formalism introduced in the paper [5] to compute correlation functions in the AdS/CFT correspondence. We show how the on-shell action of a scalar field in a compactification of AdS space can be obtained by flowing in the space of (non-local) theories with different sizes of the extra-dimension. Our method is relevant in particular for holographic computations in the Randall-Sundrum scenario with one or two branes and it allows the inclusion of brane-localized actions in a systematic way. The method can also be generalized to other backgrounds and does not rely on explicit knowledge of the solutions of the wave-equations.

We discuss the sizes of a black hole in the M theory pp-wave background, and how the transverse size can be reproduced in the matrix model.

RR fluxes representing different cohomology classes may correspond to the same twisted K-theory class. We argue that such fluxes are related by monodromies, generalizing and sometimes T-dual to the familiar monodromies of a D7-brane. A generalized ``theta angle'' is also transformed, but changes by a multiple of 2π. As an application, NS5-brane monodromies modify the twisted K-theory classification of fluxes. Furthermore, in the noncompact case K-theory does not distinguish flux configurations in which dG is nontrivial in compactly supported cohomology. Such fluxes are realized as the decay products of unstable D-branes that wrapped nontrivial cycles. This is interpreted using the E₈ bundle formalism.

The correlation functions of open Wilson line operators in two-dimensional Yang-Mills theory on the noncommutative torus are computed exactly. The correlators are expressed in two equivalent forms. An instanton expansion involves only topological numbers of Heisenberg modules and enables extraction of the weak-coupling limit of the gauge theory. A dual algebraic expansion involves only group theoretic quantities, winding numbers and translational zero modes, and enables analysis of the strong-coupling limit of the gauge theory and the high-momentum behaviour of open Wilson lines. The dual expressions can be interpreted physically as exact sums over contributions from virtual electric dipole quanta.

We give a simple interpretation of the recent solutions for cosmologies with a transient accelerating phase obtained from compactification in hyperbolic manifolds, or from S-brane solutions of string/M-theory. In the four-dimensional picture, these solutions correspond to bouncing the radion field off its exponential potential. Acceleration occurs at the turning point, when the radion stops and the potential energy momentarily dominates. The virtues and limitations of these approaches become quite transparent in this interpretation.

We present new results for the matrix elements of the Q₆ and Q₄penguin operators, evaluated in a large-N_capproach which incorporates important (N_c²n_f/N_c) unfactorized contributions. Our approach shows analytic matching between short- and long-distance scale dependences within dimensional renormalization schemes, such as . Numerically, we find that there is a large positive contribution to the ΔI = 1/2 matrix element of Q₆and hence to the direct CP-violation parameter ε'/ε. We also present results for the ΔI = 1/2 rule in K→ππ amplitudes, which incorporate the related and important ``eye-diagram'' contributions of (N_c²1/N_c) from the Q₂operator (i.e. the penguin-like contraction). The results lead to an enhancement of the ΔI = 1/2 effective coupling. The origin of the large unfactorized contributions which we find is discussed in terms of the relevant scales of the problem.

There has been some evidence that the fine structure ``constant'' α may vary with time. We point out that this variation can be described by a scalar field in some supergravity theory in our toy model, for instance, the N = 8 extended supergravity in four dimensions which can be accommodated in M-theory.

Berenstein, Maldacena, and Nastase have proposed, as a limit of the strong form of the AdS/CFT correspondence, that string theory in a particular plane wave background is dual to a certain subset of operators in the = 4 super-Yang-Mills theory. Even though this is a priori a strong/weak coupling duality, the matrix elements of the string theory hamiltonian, when expressed in gauge theory variables, are analytic in the 't Hooft coupling constant. This allows one to conjecture that, like the masses of excited string states, these can be recovered using perturbation theory in Yang-Mills theory. In this paper we identify the difference between the generator of scale transformations and a particular U(1) R-symmetry generator as the operator dual to the string theory hamiltonian for nonvanishing string coupling. We compute its matrix elements and find that they agree with the string theory prediction provided that the state-operator map is modified for nonvanishing string coupling. We construct this map explicitly and calculate the anomalous dimensions of the new operators. We identify the component arising from the modification of the state-operator map with the contribution of the string theory contact terms to the masses of string states.

We propose an alternative interpretation for the meaning of noncommutativity of the string-inspired field theories and quantum mechanics. Arguments are presented to show that the noncommutativity generated in the stringy context should be assumed to be only between the particle coordinate observables, and not of the spacetime coordinates. Some implications of this fact for noncomutative field theories and quantum mechanics are discussed. In particular, a consistent interpretation is given for the wavefunction in quantum mechanics. An analysis of the noncommutative theories in the Schrödinger formulation is performed employing a generalized quantum Hamilton-Jacobi formalism. A formal structure for noncommutative quantum mechanics, richer than the one of noncommutative quantum field theory, comes out. Conditions for the classical and commutative limits of these theories have also been determined and applied in some examples.

In a recent paper [14] we have shown that the noncommutative SUSY algebra earlierly proposed in [13] has a natural interpretation and generalization in terms of a U(1) super gauge symmetry, and hence, it must be naturally realized by supersymmetric gauge theories on superspace. Here we further elaborate on this idea by considering a specific example of such models — the U(1) gauged supersymmetric sigma model with a superpotential term in D = 2, = 1 superspace — and investigate the conditions under which the classical dynamics allows for the realization of a central charge in its associated generalized superalgebra. This realization accounts for an elegant interpretation of the central charge as a U(1) charge for the elementary excitations as well as for the solitonic (BPS) solutions of the model under consideration.

Employing the string bit formalism of [18], we identify the basis transformation that relates BMN operators in = 4 gauge theory to string states in the dual string field theory at finite g₂ = J²/N. In this basis, the supercharge truncates at linear order in g₂, and the mixing amplitude between 1 and 2-string states precisely matches with the (corrected) answer of [5] for the 3-string amplitude in light-cone string field theory. Supersymmetry then predicts the order g₂² contact term in the string bit hamiltonian. The resulting leading order mass renormalization of string states agrees with the recently computed shift in conformal dimension of BMN operators in the gauge theory.

We study supersymmetric intersections of M2 and M5 branes with different pp-waves of M-theory. We consider first M-brane probes in the background of pp-waves and determine under which conditions the embedding is supersymmetric. We particularize our formalism to the case of pp-waves with 32, 24 and 20 supersymmetries. We also construct supergravity solutions for the brane-wave system. Generically these solutions are delocalised along some directions transverse to the brane and preserve the same number of supersymmetries as in the brane probe approach.

We study Born-Infeld type tachyonic effective action of unstable D2-brane with a runaway potential and find rich structure of static regular solitonic solutions. There exists only periodic array of tachyon kink-antikinks in pure tachyonic theory, however, in the presence of electromagnetic fields, solutions include periodic arrays, topological tachyon kinks, half kink, and bounces. Computed tension of each kink or single unit of the periodic array has T₁ = (2)^1/2πT₂ or that with a multiplicative factor depending on electric field. When both electric and magnetic fields are turned on, fundamental string charge density has a confined component in addition to a constant piece. These evidences imply that the obtained codimension-1 objects are likely to be interpreted as D1-brane (and D1F1) or array of D1D-bar1 (and D1F1-D-barF1) as was the case without the electromagnetic fields. Generalization to unstable Dp-branes is straightforward.

Higher spin tensor gauge fields have natural gauge-invariant field equations written in terms of generalised curvatures, but these are typically of higher than second order in derivatives. We construct geometric second order field equations and actions for general higher spin boson fields, and first order ones for fermions, which are non-local but which become local on gauge-fixing, or on introducing auxiliary fields. This generalises the results of Francia and Sagnotti to all representations of the Lorentz group.

The spectrum and degeneracies of the Dirac operator are analysed on compact coset spaces when there is a non-zero homogeneous background gauge field which is compatible with the symmetries of the space, in particular when the gauge field is derived from the spin-connection. It is shown how the degeneracy of the lowest Landau level in the recently proposed higher dimensional quantum Hall effect is related to the Atiyah-Singer index theorem for the Dirac operator on a compact coset space.

The classical theory for a massive free particle moving on the group manifold AdS₃≅SL(2,) is analysed in detail. In particular a symplectic structure and two different sets of canonical coordinates are explicitly found, corresponding to the Cartan and Iwasawa decomposition of the group. Canonical quantization is performed in two different ways; by imposing the future-directed constraint before and after quantization. It is found that this leads to different quantum theories. The Hilbert space of either theory decomposes into the sum of certain irreducible representations of sl(2,)⊕sl(2,); however, depending on how the constraint is imposed we get different representations. Quantization of the mass occurs, although a continuum exists in the unconstrained theory corresponding to particles that can reverse their direction in time. A quantization in terms of the ``chiral'' variables of the theory is also carried out giving the same results. Comparisons are made between QFT in AdS₃ and the quantum mechanics derived, and it is found that one of the quantum theories is consistent with the Breitenlohner-Freedman bound.

We perform a complete global phenomenological analysis of a realistic string-inspired model based on the supersymmetric Pati-Salam SU(4) × SU(2)_L × SU(2)_R gauge group supplemented by a U(1) family symmetry, and present predictions for all observables including muon g−2,τ→μγ, and the CHOOZ angle. Our analysis demonstrates the compatibility of such a model with all laboratory data including charged fermion masses and mixing angles, LMA MSW and atmospheric neutrino masses and mixing angles, and b→sγ, allowing for small deviations from third family Yukawa unification. We show that in such models the squark and slepton masses may be rather light compared to similar models with exact Yukawa unification.

There are currently many string inspired conjectures about the structure of the low-energy effective action for super Yang-Mills theories which require explicit multi-loop calculations. In this paper, we develop a manifestly covariant derivative expansion of superspace heat kernels and present a scheme to evaluate multi-loop contributions to the effective action in the framework of the background field method. The crucial ingredient of the construction is a detailed analysis of the properties of the parallel displacement propagators associated with Yang-Mills supermultiples in -extended superspace.

We give examples of string compactifications to 4d Minkowski space with different amounts of supersymmetry that can be connected by spherical domain walls. The tension of these domain walls is tunably lower than the 4d Planck scale. The ``stringy'' description of these walls is known in terms of certain configurations of wrapped Dirichlet and NS branes. This construction allows us to connect a variety of vacua with 4d = 4,3,2,1 supersymmetry.

We compute the three point correlation functions for primordial scalar and tensor fluctuations in single field inflationary models. We obtain explicit expressions in the slow roll limit where the answer is given terms of the two usual slow roll parameters. In a particular limit the three point functions are determined completely by the tilt of the spectrum of the two point functions. We also make some remarks on the relation of this computation to dS/CFT and AdS/CFT. We emphasize that (A)dS/CFT can be viewed as a statement about the wavefunction of the universe.

We study deep inelastic scattering in gauge theories which have dual string descriptions. As a function of gN we find a transition. For small gN, the dominant operators in the OPE are the usual ones, of approximate twist two, corresponding to scattering from weakly interacting partons. For large gN, double-trace operators dominate, corresponding to scattering from entire hadrons (either the original `valence' hadron or part of a hadron cloud.) At large gN we calculate the structure functions. As a function of Bjorken x there are three regimes: x of order one, where the scattering produces only supergravity states; x small, where excited strings are produced; and, x exponentially small, where the excited strings are comparable in size to the AdS space. The last regime requires in principle a full string calculation in curved spacetime, but the effect of string growth can be simply obtained from the world-sheet renormalization group.

We discuss type-IIB orientifolds with D-branes, and NSNS and RR field strength fluxes. The D-brane sectors lead to open string spectra with non-abelian gauge symmetry and charged chiral fermions. The closed string field strengths generate a scalar potential stabilizing most moduli. We describe the construction of models with = 1 supersymmetric subsectors in the context of orientifolds of IIB theory on T⁶/(₂ × ₂), containing D9-branes with world-volume magnetic fluxes, and illustrate model building possibilities with several explicit examples. We comment on a T-dual picture with D8-branes on non-Calabi-Yau half-flat geometries, and discuss some of the topological properties of such configurations. We also explore the construction of models with fluxes and with D3-branes at singularities and present a non-supersymmetric 3-family SU(5) model.

We introduce a notion of universality classes for the Gregory-Laflamme instability and determine, in the supergravity approximation, the stability of a variety of solutions, including the non-extremal D3-brane, M2-brane, and M5-brane. These three non-dilatonic branes cross over from instability to stability at a certain non-extremal mass. Numerical analysis suggests that the wavelength of the shortest unstable mode diverges as one approaches the cross-over point from above, with a simple critical exponent which is the same in all three cases.

It has been shown by Polchinski and Strassler that the scaling of high energy QCD scattering amplitudes can be obtained from string theory. They considered an AdS slice as an approximation for the dual space of a confining gauge theory. Here we use this approximation to estimate in a very simple way the ratios of scalar glueball masses imposing Dirichlet boundary conditions on the string dilaton field. These ratios are in good agreement with the results in the literature. We also find that they do not depend on the size of the slice.

Some recent studies have considered a Randall-Sundrum-like brane world evolving in the background of an anti-de Sitter Reissner-Nordstrom black hole. For this scenario, it has been shown that, when the bulk charge is non-vanishing, a singularity-free ``bounce'' universe will always be obtained. However, for the physically relevant case of a de Sitter brane world, we have recently argued that, from a holographic (c-theorem) perspective, such brane worlds may not be physically viable. In the current paper, we reconsider the validity of such models by appealing to the so-called ``causal entropy bound''. In this framework, a paradoxical outcome is obtained: these brane worlds are indeed holographically viable, provided that the bulk charge is not too small. We go on to argue that this new finding is likely the more reliable one.

We present results for the coupling of the light vector mesons to the tensor current, relative to the standard vector meson decay constants. From an (a)-improved lattice study, performed at three values of the lattice spacing in the quenched approximation, our final values (in the continuum limit), in the MS-bar scheme at μ = 2 GeV, are: f_ρ^T/f_ρ = 0.72(2)(⁺²₋₀), f_K*^T/f_K* = 0.74(2), f_ϕ^T/f_ϕ = 0.76(1).

In this note we provide an explicit example of type-IIB supersymmetric D3-branes solution on a pp-wave like background, consisting in the product of an eight-dimensional pp-wave times a two-dimensional flat space. An interesting property of our solution is the fully localization of the D3-branes (i.e. the solution depends on all the transverse coordinates). Then we show the generalization to other Dp-branes and to the D1/D5 system.

We show that the source of RR field computed from the boundary state describing the decay of a non-BPS brane is reproduced by a particular form of the Wess-Zumino term in the tachyon effective action. We also obtain a simple expression of the S-charge associated with rolling tachyons.

We consider the GSO(−) sector of the open superstring using the formalism with four-dimensional hybrid variables. This sector is defined by the world sheet hybrid variables (θ^α,) with antiperiodic boundary conditions. The corresponding spectrum of states and conditions for physical vertices are described. In particular we construct explicitly the lower level GSO(−) vertex operators corresponding to the tachyon and the massless fermions. Using these new vertices, the tachyon and massless sector contribution to the superstring field theory action of Berkovits is evaluated. In this way we have included the Ramond sector and we end by discussing some features of the action.

We compute the density of open strings stretching between AdS₂ branes in the euclidean AdS₃. This is done by solving the factorization constraint of a degenerate boundary field, and the result is checked by a Cardy-type computation. We mention applications to branes in the minkowskian AdS₃ and its cigar coset.

Liouville field theory on an unoriented surface is investigated, in particular, the one point function on a ² is calculated. The constraint of the one point function is obtained by using the crossing symmetry of the two point function. There are many solutions of the constraint and we can choose one of them by considering the modular bootstrap.

We have covariantized the lagrangians of the U(1)_V × U(1)_A models, which have U(1)_V × U(1)_A gauge symmetry in two dimensions, and studied their symmetric structures. The special property of the U(1)_V × U(1)_A models is the fact that all these models have an extra time coordinate in the target space-time. The U(1)_V × U(1)_A models coupled to two-dimensional gravity are string models in 26+2 dimensional target space-time for bosonic string and in 10+2 dimensional target space-time for superstring. Both string models have two time coordinates. In order to construct the covariant lagrangians of the U(1)_V × U(1)_A models the generalized Chern-Simons term plays an important role. The supersymmetric generalized Chern-Simons action is also proposed. The Green-Schwarz type of U(1)_V × U(1)_A superstring model has another fermionic local symmetry as well as κ-symmetry. The supersymmetry of target space-time is different from the standard one.