Multiple phases and meromorphic deformations of unitary matrix models

TL;DR

This paper analyzes a complex unitary matrix model with multiple phases, phase transitions, and meromorphic deformations, revealing detailed phase diagrams and physical phenomena such as tunneling and symmetry breaking.

Contribution

It introduces a detailed phase diagram for a unitary matrix model with determinant insertions and explores meromorphic deformations with non-trivial phase structures.

Findings

Identifies five distinct phases including gapped and ungapped.

Characterizes phase transition orders: third and second.

Studies meromorphic deformations with symplectic singularities.

Abstract

We study a unitary matrix model with Gross-Witten-Wadia weight function and determinant insertions. After some exact evaluations, we characterize the intricate phase diagram. There are five possible phases: an ungapped phase, two different one-cut gapped phases and two other two-cut gapped phases. The transition from the ungapped phase to any gapped phase is third order, but the transition between any one-cut and any two-cut phase is second order. The physics of tunneling from a metastable vacuum to a stable one and of different releases of instantons is discussed. Wilson loops, $\beta$-functions and aspects of chiral symmetry breaking are investigated as well. Furthermore, we study in detail the meromorphic deformation of a general class of unitary matrix models, in which the integration contour is not anchored to the unit circle. The ensuing phase diagram is characterized by symplectic singularities and captured by a Hasse diagram.