Four-dimensional $\mathcal N=2$ superconformal long circular quivers

TL;DR

This paper computes nonplanar corrections to key observables in four-dimensional $ =2$ superconformal circular quiver theories, revealing their asymptotic behaviors and linking them to an integrable lattice model.

Contribution

It provides a closed-form expression for leading nonplanar corrections in long quivers, connecting localization results to integrable models and analyzing their asymptotic properties.

Findings

Derived a closed-form for nonplanar corrections in large quivers.

Identified different asymptotic behaviors depending on parameter limits.

Linked the corrections to properties of an integrable lattice model.

Abstract

We study four-dimensional $\mathcal N=2$ superconformal circular, cyclic symmetric quiver theories which are planar equivalent to $\mathcal N=4$ super Yang-Mills. We use localization to compute nonplanar corrections to the free energy and the circular half-BPS Wilson loop in these theories for an arbitrary number of nodes, and examine their behaviour in the limit of long quivers. Exploiting the relationship between the localization quiver matrix integrals and an integrable Bessel operator, we find a closed-form expression for the leading nonplanar correction to both observables in the limit when the number of nodes and 't Hooft coupling become large. We demonstrate that it has different asymptotic behaviour depending on how the two parameters are compared, and interpret this behaviour in terms of properties of a lattice model defined on the quiver diagram.