Table of contents

It is shown that a pair of vortex and anti-vortex is completely screened in 2+1 dimensional Yang-Mills theory and 3+1 dimensional Yang-Mills theory in the strong coupling limit, based on the recent conjecture of Maldacena. This is consistent with the fact that these theories exhibit confinement.

The one-instanton contributions to various correlation functions of superconformal currents in four-dimensional = 4 supersymmetric SU(2) Yang-Mills theory are evaluated to the lowest order in perturbation theory. Expressions of the same form are obtained from the leading effects of a single D-instanton extracted from the IIB superstring effective action around the AdS₅ × S⁵ background. This is in line with the suggested AdS/Yang-Mills correspondence. The relation between Yang-Mills instantons and D-instantons is further confirmed by the explicit form of the classical D-instanton solution in the AdS₅ × S⁵ background and its associated supermultiplet of zero modes. Speculations are made concerning instanton effects in the large-N_c limit of the SU(N_c) Yang-Mills theory.

A coincident D-brane - anti-D-brane pair has a tachyonic mode. We present an argument showing that at the classical minimum of the tachyonic potential the negative energy density associated with the potential exactly cancels the sum of the tension of the brane and the anti-brane, thereby giving a configuration of zero energy density and restoring space-time supersymmetry.

Actions for branes, with or without worldsurface gauge fields, are discussed in a unified framework. A simple algorithm is given for constructing the component Green-Schwarz actions. Superspace actions are also discussed. Three examples are given to illustrate the general procedure: the membrane in D = 11 and the D2-brane, which both have on-shell worldsurface supermultiplets, and the membrane in D = 4, which has an off-shell multiplet.

S-duality symmetry of type IIB string theory predicts the existence of a stable non-BPS state on an orbifold five plane of the type IIB theory if the orbifold group is generated by the simultaneous action of (−1)^F_L and the reversal of sign of the four coordinates transverse to the orbifold plane. We calculate the mass of this state by starting from a pair of D-strings carrying the same charge as this state, and then identifying the point in the moduli space where this pair develops a tachyonic mode, signalling the appearance of a bound state of this configuration into the non-BPS state.

We point out certain unexpected features of the planar QCD₃ confining potential, as computed from a classical worldsheet action in an AdS metric via the Maldacena conjecture. We show that there is no Lüscher c/R term in the static-quark potential, which is contrary to both the prediction of various effective string models, and the results of some recent lattice Monte Carlo studies. It is also noted that the glueball masses extracted from classical supergravity tend to finite, coupling-independent constants in the strong coupling limit, even as the string tension tends to infinity in the same limit; this is a counter-intuitive result.

An explicit relativistic light-front quark model is presented which gives the momentum transfer dependent form factors of weak hadronic currents among heavy pseudoscalar and vector mesons in the whole accessible kinematical region 0 ⩽ q² ⩽ q²_max. It is shown that in the limit of infinite masses of active quarks these form factors can be expressed in terms of universal Isgur- Wise function. The explisit expression for this function is obtained. It is shown that neglect of pair creation from the vacuum in calculations of form factors does not violate Luke's theorem.

We study spatially homogeneous and isotropic solutions to the equations of motion derived from dilaton gravity, in the presence of a special combination of higher derivative terms in the gravitational action. All solutions are nonsingular. For initial conditions resembling those in the pre-big-bang scenario, there are solutions corresponding to a spatially flat, bouncing Universe originating in a dilaton-dominated contracting phase and emerging as an expanding Friedmann Universe.

We study the BPS spectrum of supersymmetric 5 dimensional field theories and their representations as string webs. It is found that a state of given charges exists when it has a representation as an irreducible string web. Its spin is determined by the string web. The number of fermionic zero modes is 8g+4b, where g is the number of internal faces and b is the number of boundaries. In the lift to M theory of 4d field theories such states are described by membranes ending on the 5-brane, breaking SUSY from 8 to 4, and g becomes the genus of the membrane. Mathematically, we obtain a diagrammatic method to find the spectrum of curves on a toric complex surface, and the number of their moduli.

We consider Type IIB superstring theory with the addition of n 9-branes and n anti-9-branes (and no orientifolds). The result is a ten-dimensional chiral theory of open and closed oriented strings with gauge group U(n) × U(n). There is, however, a tachyonic instability which can be understood as the consequence of brane-antibrane annihilation. We therefore expect to recover the usual IIB theory as the tachyon rolls to infinity.

We present a model-independent analysis of K⁺→π⁺ℓ⁺ℓ⁻ and K_S→π⁰ℓ⁺ℓ⁻ decays, including K→3π unitarity corrections and a general decomposition of the dispersive amplitude. From the existing data on K⁺→π⁺e⁺e⁻ we predict the ratio R = B(K⁺→π⁺μ⁺μ⁻)/B(K⁺→π⁺e⁺e⁻) to be larger than 0.23, in slight disagreement with the recent measurementR = 0.167±0.036. Consequences for the K^±→π^±e⁺e⁻ charge asymmetries and for the K_L→π⁰e⁺e⁻ mode are also discussed.

Extremal six-dimensional black string solutions with some non-trivial momentum distribution along the wave are considered. These solutions were recently shown to contain a singularity at the would-be position of the event horizon. In the black string geometry, all curvature invariants are finite at the horizon. It is shown that if the effects of infalling matter are included, there are curvature invariants which diverge there. This implies that quantum corrections will be important at the would-be horizon. The effect of this singularity on test strings is also considered, and it is shown that it leads to a divergent excitation of the string. The quantum corrections will therefore be important for test objects.

We study the (p,q)5-brane dynamics from the viewpoint of Matrix string theory in the T-dualized ALE background. The most remarkable feature in the (p,q)5-brane is the existence of ``fractional string'', which appears as the instanton of 5-brane gauge theory. We approach to the physical aspects of fractional string by means of the two types of Matrix string probes: One of which is that given in Witten (New ``gauge'' theories in six dimensions, JHEP01(1998)001 [hep-th/9710065]).

As the second probe we present the Matrix string theory describing the fractional string itself. We calculate the moduli space metrics in the respective cases and argue on the specific behaviors of fractional string. Especially, we show that the ``joining'' process of fractional strings can be realized as the transition from the Coulomb branch to the Higgs branch of the fractional string probe. In this argument, we emphasize the importance of some monodromies related with the θ-angle of the 5-brane gauge theory.

Over the years, many jet clustering algorithms have been proposed for the analysis of hadronic final states in e⁺e⁻ annihilations. These have somewhat different emphasis and are therefore more or less suited for various applications. We here review some of the most used and compare them from a theoretical and experimental point of view.