Asymptotic bootstrap for unitary matrix integrals at complex coupling

TL;DR

This paper introduces an asymptotic bootstrap method for high-precision, non-perturbative analysis of unitary matrix integrals, effectively capturing instanton effects and phase structures in complex coupling spaces.

Contribution

The paper presents a novel asymptotic bootstrap approach combining recursion and asymptotic control, enabling precise non-perturbative studies of unitary matrix models without positivity constraints.

Findings

Accurate computation of Wilson loop expectation values including instanton effects.

Validation of numerical results against analytical instanton calculations.

Identification of Stokes lines as proxies for phase boundaries in complex coupling space.

Abstract

We apply an asymptotic bootstrap estimate method to the non-perturbative study of unitary matrix integrals. The method combines exact recursion relations with asymptotic control of large modes to achieve very high numerical precision without relying on positivity or semidefinite programming. We demonstrate its effectiveness in large-$N$ unitary matrix models by computing Wilson loop expectation values with sensitivity to exponentially small instanton effects and validating them against analytical instanton calculations. We further use the method to explore phase diagrams of unitary matrix models in complex 't Hooft coupling space, where positivity is absent, and observe that Stokes lines provide a useful proxy for additional phase boundaries. Our results show that asymptotic bootstrap estimates offer a practical and precise tool for probing the non-perturbative structure of unitary matrix integrals.