The Hilbert series of U/SU SQCD and Toeplitz Determinants

TL;DR

This paper introduces a novel method to compute the Hilbert series of N=1 supersymmetric QCD using Toeplitz determinants, providing exact and asymptotic results for various gauge groups and flavor numbers.

Contribution

It develops a new technique linking Hilbert series computation to Toeplitz determinants, enabling exact and asymptotic calculations in supersymmetric QCD.

Findings

Derived exact Hilbert series for specific gauge groups.

Established asymptotic formulas for large numbers of colors and flavors.

Connected Hilbert series computation with random matrix theory.

Abstract

We present a new technique for computing Hilbert series of N=1 supersymmetric QCD in four dimensions with unitary and special unitary gauge groups. We show that the Hilbert series of this theory can be written in terms of determinants of Toeplitz matrices. Applying related theorems from random matrix theory, we compute a number of exact Hilbert series as well as asymptotic formulae for large numbers of colours and flavours -- many of which have not been derived before.