Tracy-Widom distribution in four-dimensional super-Yang-Mills theories

TL;DR

This paper explores the exact computation of observables in 4D superconformal Yang-Mills theories using Fredholm determinants, analyzing their dependence on the coupling constant and addressing nonperturbative effects through resurgent transseries.

Contribution

It introduces a novel method to compute nonperturbative corrections in strong coupling expansions of super-Yang-Mills theories via Fredholm determinants and resurgent analysis.

Findings

Exact Fredholm determinant representations for observables

Identification of factorial divergence in strong coupling expansions

Development of a systematic approach for nonperturbative corrections

Abstract

Various observables in different four-dimensional superconformal Yang-Mills theories can be computed exactly as Fredholm determinants of truncated Bessel operators. We exploit this relation to determine their dependence on the 't Hooft coupling constant. Unlike the weak coupling expansion, which has a finite radius of convergence, the strong coupling expansion is factorially divergent, necessitating the inclusion of nonperturbative, exponentially small corrections. We develop a method to systematically compute these corrections and discuss the resurgent properties of the resulting transseries.