Exploring superconformal Yang-Mills theories through matrix Bessel kernels

TL;DR

This paper studies exact computations of observables in superconformal Yang-Mills theories using matrix Bessel kernels, revealing their weak and strong coupling behaviors and non-perturbative corrections.

Contribution

It introduces a unifying determinant representation for observables via matrix Bessel operators and analyzes their coupling expansions and non-perturbative effects.

Findings

Weak-coupling expansion has finite radius of convergence.

Strong-coupling expansion shows factorial divergence.

Non-perturbative corrections resemble a mass gap expansion.

Abstract

A broad class of observables in four-dimensional $\mathcal{N}=2$ and $\mathcal{N}=4$ superconformal Yang-Mills theories can be exactly computed for arbitrary 't Hooft coupling as Fredholm determinants of integrable Bessel operators. These observables admit a unifying description through a one-parameter generating function, which possesses a determinant representation involving a matrix generalization of the Bessel operator. We analyze this generating function over a wide range of parameter values and finite 't Hooft coupling. We demonstrate that it has a well-behaved weak-coupling expansion with a finite radius of convergence. In contrast, the strong-coupling expansion exhibits factorially growing coefficients, necessitating the inclusion of non-perturbative corrections that are exponentially suppressed at strong coupling. We compute these non-perturbative corrections and observe a striking resemblance between the resulting trans-series expansion of the generating function and the partition function of a strongly coupled theory expanded in powers of a mass gap.