Shimon Yankielowicz

Supersymmetric QCD and its massless limit: An effective lagrangian analysis

Abstract Supersymmetric QCD is studied by an effective lagrangian method. When all flavours are massive supersymmetric vacua, reproducing the known value of Wittens index, do exist and decoupling of heavy flavours occurs When one or more flavours become massless, some chirality breaking order parameters run to infinity suggesting a non-smooth zero mass limit, in contrast with the case of ordinary QCD. Possible implications of these results on chiral and/or supersymmetry breaking patterns in the massless theory are briefly discussed.

Wilson Loops in the Large N Limit at Finite Temperature

Using a proposal of Maldacena we compute in the framework of the supergravity description of N coincident D3 branes the energy of a quark anti-quark pair in the large N limit of U(N) N=4 SYM in four dimensions at finite temperature.

Wilson loops, confinement, and phase transitions in large N gauge theories from supergravity

We use the recently proposed supergravity approach to large N gauge theories to calculate ordinary and spatial Wilson loops of gauge theories in various dimensions. In this framework we observe an area law for spatial Wilson loops in four and five dimensional supersymmetric Yang-Mills at finite temperature. This can be interpreted as the area law of ordinary Wilson loops in three and four dimensional non-supersymmetric gauge theories at zero temperature which indicates confinement in these theories. Furthermore, we show that super Yang Mills theories with 16 supersymmetries at finite temperature do not admit phase transitions between the weakly coupled super Yang Mills and supergravity regimes. This result is derived by analyzing the entropy and specific heat of those systems as well as by computing ordinary Wilson loops at finite temperature. The calculation of the entropy was carried out in all different regimes and indicates that there is no first order phase transition in these systems. For the same theories at zero temperature we also compute the dependence of the quark anti-quark potential on the separating distance.

Diffeomorphisms and Holographic Anomalies

Using the relation between diffeomorphisms in the bulk and Weyl transformations on the boundary, we study the Weyl transformation properties of the bulk metric on-shell and of the boundary action. We obtain a universal formula for one of the classes of trace anomalies in any even dimension in terms of the parameters of the gravity action.

Simple Currents, Modular Invariants and Fixed Points

We review the use of simple currents in constructing modular invariant partition functions and the problem of resolving their fixed points. We present some new results, in particular regarding fixed point resolution. Additional empirical evidence is provided in support of our conjecture that fixed points are always related to some conformal field theory. We complete the identification of the fixed point conformal field theories for all simply laced and most non-simply laced Kac-Moody algebras, for which the fixed point CFT’s turn out to be Kac-Moody algebras themselves. For the remaining non-simply laced ones we obtain spectra that appear to correspond to new non-unitary conformal field theories. The fusion rules of the simplest unidentified example are computed.

On the relation between the holomorphic prepotential and the quantum moduli in SUSY gauge theories

We give a simple proof of the relation AanF = &bl (Tr #2), which is vaiid for N = 2 super-symmetric QCD with massless quarks. We consider SU( NC) gauge theories as well as SO( NC) and SP ( NC). An analogous relation which corresponds to massive hypermultiplets is written down. We also discuss the generalizations to N = 1 models in the Coulomb phase.

On exactly marginal deformations of N=4 SYM and type IIB supergravity on AdS(5) x S**5

= 4 supersymmetric Yang-Mills theory with gauge group SU(N) (N ≥ 3) is believed to have two exactly marginal deformations which break the supersymmetry to = 1. We discuss the construction of the string theory dual to these deformations, in the supergravity approximation, in a perturbation series around the AdS5 × S5 solution. We construct explicitly the deformed solution at second order in the deformation. We show that deformations which are marginal but not exactly marginal lead to a non-conformal solution with a logarithmically running coupling constant. Surprisingly, at third order in the deformation we find the same beta functions for the couplings in field theory and in supergravity, suggesting that the leading order beta functions (or anomalous dimensions) do not depend on the gauge coupling (the coefficient is not renormalized).

Comments on the M theory approach to N = 1 SQCD and brane dynamics

Abstract We use the M theory approach of Witten to investigate N = 1 SU( N c ) SQCD with N f flavors. We reproduce the field theoretical results and identify in M theory the gluino condensate and the eigenvalues of the meson matrix. This approach allows us to identify the constant piece of the effective field theory coupling from which the coefficient of the one-loop β-function can be identified. By studying the area of the M-theory five-brane we investigate the stability of type IIA brane configurations. We prove that in a supersymmetric setup there is no force between static D4-branes that end on NS five-branes. The force in the case that there is a relative velocity between the branes is computed. We show that at the regions of intersecting IIA branes the curvature of the M theory five-brane is singular in the type IIA limit.

M-theory and Seiberg-Witten curves: orthogonal and symplectic groups

We discuss N = 2 supersymmetric type IIA brane configurations within M-theory. This is a generalization of the work of Witten to all classical groups. (~) 1997 Published by Elsevier Science B.V.

INTERACTIONS OF STRINGS AND D-BRANES FROM M THEORY

We discuss the relation between M theory and type II string theories. We show that, assuming “natural” interactions between membranes and fivebranes in M theory, the known interactions between strings and D-branes in type II string theories arise in appropriate limits. Our discussion of the interactions is purely at the classical level. We remark on issues associated with the M theory approach to enhanced gauge symmetries, which deserve further investigation.