Vacua of N=1 Supersymmetric QCD from Spin Chains and Matrix Models

TL;DR

This paper explores the vacuum structure of N=1 supersymmetric QCD with fundamental hypermultiplets using integrable spin chains and matrix models, establishing their equivalence under specific coupling relations.

Contribution

It demonstrates the equivalence of spin chain and matrix model approaches to analyzing vacua in N=1 SQCD with fundamental matter, including detailed analysis for SU(2) with N_f=4.

Findings

Spin chain Hamiltonian matches the effective superpotential from the matrix model.

The two approaches agree when couplings are related via instanton series.

Detailed analysis provided for the SU(2) gauge group with four flavors.

Abstract

We consider the vacuum structure of the finite N=2 theory with N_f=2N fundamental hypermultiplets broken to N=1 by a superpotential for the adjoint chiral multiplet. We do this in two ways: firstly, by compactification to three dimensions, in which case the effective superpotential is the Hamiltonian of an integrable spin chain. In the second approach, we consider the Dijkgraaf-Vafa holomorphic matrix model. We prove that the two approaches agree as long as the couplings of the two theories are related in a particular way involving an infinite series of instanton terms. The case of gauge group SU(2) with N_f=4 is considered in greater detail.