On string tensions in supersymmetric gauge theory

In some models of N=1 supersymmetric SU(M) gauge dynamics (Nucl. Phys. B 447 (1995) 271 and Nucl. Phys. B 513 (1998) 87), the tension of a string ending on q external quarks is proportional to sin(πq/M), q=1,…,M−1. In this Letter 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 an S3 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 an S2⊂S3 with q units of world volume flux. For one of the gravity dual backgrounds (Maldacena–Nuñez) a D3-brane probe calculation exactly reproduces the sin(πq/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.