New results for the SQCD Hilbert series

TL;DR

This paper presents new explicit formulas for the Hilbert series of N=1 supersymmetric QCD with U(N_c) and SU(N_c) gauge groups, employing methods from Schur polynomial expansions and random matrix theory.

Contribution

It introduces novel explicit results for the Hilbert series of SQCD using two advanced mathematical techniques previously applied in string theory contexts.

Findings

Derived new explicit formulas for the Hilbert series of SQCD.

Applied Schur polynomial expansions and log-gas methods to gauge theories.

Enhanced computational tools for analyzing supersymmetric gauge theories.

Abstract

We derive new explicit results for the Hilbert series of N=1 supersymmetric QCD with U(N_c) and SU(N_c) color symmetry. We use two methods which have previously been applied to similar computational problems in the analysis of decay of unstable D-branes: expansions using Schur polynomials, and the log-gas approach related to random matrix theory.