Strong coupling expansion in $\mathbf{\mathcal N=2}$ superconformal theories and the Bessel kernel

TL;DR

This paper develops a strong coupling expansion technique for certain $ =2$ superconformal theories using a Bessel kernel representation, revealing non-perturbative effects and extending previous results in the context of AdS/CFT correspondence.

Contribution

It introduces a novel approach to compute strong 't Hooft coupling expansions in $ =2$ superconformal models via Fredholm determinants of Bessel operators, generalizing prior partial results.

Findings

Derived strong-coupling expansions for free energy, Wilson loops, and correlators.

Identified Borel singularities indicating the need for non-perturbative corrections.

Determined non-perturbative corrections to four-point correlators in $ =4$ SYM.

Abstract

We consider strong 't Hooft coupling expansion in special four-dimensional $\mathcal N=2$ superconformal models that are planar-equivalent to $\mathcal N=4$ super Yang-Mills theory. Various observables in these models that admit localization matrix model representation can be expressed at large $N$ in terms of a Fredholm determinant of a Bessel operator. The latter previously appeared in the study of level spacing distributions in matrix models and, more recently, in four-point correlation functions of infinitely heavy half-BPS operators in planar $\mathcal N=4$ SYM. We use this relation and a suitably generalized Szego-Akhiezer-Kac formula to derive the strong 't Hooft coupling expansion of the leading corrections to free energy, half-BPS circular Wilson loop, and certain correlators of chiral primaries operators in the $\mathcal N=2$ models. This substantially generalizes partial results in the literature and represents a challenge for dual string theory calculations in AdS/CFT context. We also demonstrate that the resulting strong-coupling expansions suffer from Borel singularities and require adding non-perturbative, exponentially suppressed corrections. As a byproduct of our analysis, we determine the non-perturbative correction to the above mentioned four-point correlator in planar $\mathcal N=4$ SYM.