Classical group matrix models and universal criticality

TL;DR

This paper extends the Gross--Witten--Wadia matrix model to orthogonal and symplectic groups, revealing a universal phase transition behavior in the large N limit through Coulomb gas and character polynomial techniques.

Contribution

It introduces a generalized analysis of classical group matrix models, demonstrating universal critical behavior across different gauge groups using advanced mathematical methods.

Findings

Free energy in orthogonal and symplectic models is twice that of the unitary case in the large N limit.

The phase transition universality holds for arbitrary coupling constants.

The model links to random partitions via the Schur measure, confirming universality.

Abstract

We study generalizations of the Gross--Witten--Wadia unitary matrix model for the special orthogonal and symplectic groups. We show using a standard Coulomb gas treatment -- employing a path integral formalism for the ungapped phase and resolvent techniques for the gapped phase with one coupling constant -- that in the large $N$ limit, the free energy normalized modulo the square of the gauge group rank is twice the value for the unitary case. Using generalized Cauchy identities for character polynomials, we then demonstrate the universality of this phase transition for an arbitrary number of coupling constants by linking this model to the random partition based on the Schur measure.