Unitary matrix with a Penner-like potential also yields N_f=2

TL;DR

This paper proves that a unitary matrix model with a Penner-like potential reproduces the prepotential of N=2 SU(2) SUSY gauge theory with N_f=2, confirming a conjecture and extending known results from hermitian models.

Contribution

It provides a rigorous proof that a unitary matrix model with a Penner-like potential yields the same prepotential as the hermitian model, with slight differences in parameter identification.

Findings

Unitary matrix model reproduces the N=2 N_f=2 SU(2) prepotential.

Parameter identifications differ slightly from hermitian models.

Confirms and extends previous conjectures by Itoyama et al.

Abstract

It has been known for some time that a hermitian matrix model with a Penner-like potential yields as its large-N free energy the prepotential of N=2 N_f=2 SU(2) SUSY gauge theory. We give a rigorous proof that a unitary matrix model with the identical potential also yields the same prepotential, although the parameter identifications are slightly different. This result has been anticipated by Itoyama et. al.