On String Tensions in Supersymmetric SU(M) Gauge Theory
Abstract
Hanany, Strassler and Zaffaroni (HSZ) showed in hep-th/9707244 that, in the MQCD approach to confining {\cal N}=1 supersymmetric SU(M) gauge theory, 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 {\cal 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 MQCD result of HSZ, while for another (Klebanov-Strassler) we find approximate agreement. We suggest that an understanding of D-brane tensions in a IIB string sigma model with NS-NS flux, which describes the S-dual background, may lead to exact results for the q-string tensions in the gauge theory.Keywords
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