Moduli space of supersymmetric QCD in the Veneziano limit

TL;DR

This paper investigates the structure of the moduli space in 4d N=1 supersymmetric QCD using Hilbert series, revealing a Coulomb gas analogy, phase transitions, and explicit physical quantity computations.

Contribution

It introduces a novel Coulomb gas framework for analyzing the moduli space of supersymmetric QCD in the Veneziano limit, uncovering phase structure and phase transitions.

Findings

Identified two distinct phases in the Coulomb gas model.

Computed physical quantities like charge densities and free energies for each phase.

Demonstrated the existence of a third order phase transition.

Abstract

We study the moduli space of 4d N=1 supersymmetric QCD in the Veneziano limit using Hilbert series. In this limit, the numbers of colours and flavours are taken to be large with their ratio fixed. It is shown that the Hilbert series, which is a partition function of an ensemble of gauge invariant quantities parametrising the moduli space, can also be realised as a partition function of a system of interacting Coulomb gas in two dimensions. In the electrostatic equilibrium, exact and asymptotic analyses reveal that such a system exhibits two possible phases. Physical quantities, such as charge densities, free energies, and Hilbert series, associated with each phase, are computed explicitly and discussed in detail. We then demonstrate the existence of the third order phase transition in this system.