A note on S-duality for the N=1*Sp(2n) and SO(2n+1) super-Yang-Mills theories

Journal article, 2007

We study the N = 1* supersymmetric gauge theories with gauge groups Sp(2n) and SO(2n + 1). These theories are obtained for the corresponding N = 4 supersymmetric Yang-Mills theories via a mass deformation. We show that the number of quantum vacua in the Sp(2n) theory is equal to the number of quantum vacua in the SO(2n + 1) theory. This constitutes non-trivial support for S-duality between these theories. The verification of the equality of the number of quantum vacua involves a rather esoteric identity due to Ramanujan.