Complex Saddles in Two-dimensional Gauge Theory

TL;DR

This paper investigates the complex saddle point structure of 2D lattice gauge theory using the Gross-Witten-Wadia matrix model, revealing new insights into non-perturbative effects and phase transitions.

Contribution

It provides a numerical analysis of complex saddle points in 2D gauge theory and introduces a new interpretation of non-perturbative effects in the strong-coupling phase.

Findings

Confirmation of trans-series/instanton gas structure in weak coupling

Identification of complex saddle interpretation in strong coupling

Eigenvalue tunneling into the complex plane drives phase transition

Abstract

We study numerically the saddle point structure of two-dimensional (2D) lattice gauge theory, represented by the Gross-Witten-Wadia unitary matrix model. The saddle points are in general complex-valued, even though the original integration variables and action are real. We confirm the trans-series/instanton gas structure in the weak-coupling phase, and identify a new complex-saddle interpretation of non-perturbative effects in the strong-coupling phase. In both phases, eigenvalue tunneling refers to eigenvalues moving off the real interval, into the complex plane, and the weak-to-strong coupling phase transition is driven by saddle condensation.