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

TL;DR

This paper investigates S-duality in N=1* supersymmetric gauge theories with Sp(2n) and SO(2n+1) gauge groups, showing they have equal quantum vacua counts, supporting duality conjectures through a Ramanujan identity.

Contribution

It demonstrates the equality of quantum vacua in Sp(2n) and SO(2n+1) theories, providing evidence for S-duality in these supersymmetric models.

Findings

Number of quantum vacua in Sp(2n) equals that in SO(2n+1)

Supports S-duality between these theories

Uses Ramanujan's identity for verification

Abstract

We study the N=1* supersymmetric gauge theories with gauge groups Sp(2n) and SO(2n+1). These theories are obtained from 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.