On String Tensions in Supersymmetric SU(M) Gauge Theory

TL;DR

This paper calculates the ratios of string tensions in N=1 supersymmetric SU(M) gauge theories using type IIB gravity duals, confirming the sine dependence predicted by earlier models and exploring D-brane tension connections.

Contribution

It provides a gravity dual computation of q-string tension ratios in N=1 SUSY gauge theories, confirming the sine law and extending understanding of string dynamics via D-branes.

Findings

Exact sine(pi q/M) dependence in Maldacena-Nunez background

Approximate sine dependence in Klebanov-Strassler background

Connection between q-string tensions and D-brane tensions in WZW model

Abstract

In some models of N=1 supersymmetric SU(M) gauge dynamics (hep-th/9503163 and hep-th/9707244), the tension of a string ending on q external quarks is proportional to sin(pi q/M), q=1,..., M-1. In this paper we calculate the ratios of the q-string tensions using the recently derived type IIB gravity duals of N=1 SUSY gauge theories. Far in the IR these gravity duals contain a three-sphere with M units of R-R 3-form flux which, upon S-duality, turns into NS-NS 3-form flux. The confining q-string is described by a D3-brane wrapping a two-sphere inside the three-sphere with q units of world volume flux. For one of the gravity dual backgrounds (Maldacena-Nunez) a D3-brane probe calculation exactly reproduces the sin(pi q/M) dependence, while for another (Klebanov-Strassler) we find approximate agreement. We speculate on the connection of the q-string tensions with D-brane tensions in the SU(2) WZW model.