On topological recursion for Wilson loops in $\mathcal N=4$ SYM at strong coupling

TL;DR

This paper develops a novel saddle point method using topological recursion to directly analyze non-planar corrections in strongly coupled $ ext{N}=4$ SYM Wilson loops, revealing new structural insights into their genus expansion.

Contribution

It introduces a strong coupling approach based on topological recursion that bypasses finite coupling calculations, providing new proofs and structures of the genus expansion for Wilson loop observables.

Findings

Simplified form of matrix model multi-point resolvents at strong coupling

Identification of structures in the genus expansion at large tension

New results on correlators of Wilson loops and chiral operators

Abstract

We consider $U(N)$ $\mathcal N=4$ super Yang-Mills theory and discuss how to extract the strong coupling limit of non-planar corrections to observables involving the $\frac{1}{2}$-BPS Wilson loop. Our approach is based on a suitable saddle point treatment of the Eynard-Orantin topological recursion in the Gaussian matrix model. Working directly at strong coupling we avoid the usual procedure of first computing observables at finite planar coupling $\lambda$, order by order in $1/N$, and then taking the $\lambda\gg 1$ limit. In the proposed approach, matrix model multi-point resolvents take a simplified form and some structures of the genus expansion, hardly visible at low order, may be identified and rigorously proved. As a sample application, we consider the expectation value of multiple coincident circular supersymmetric Wilson loops as well as their correlator with single trace chiral operators. For these quantities we provide novel results about the structure of their genus expansion at large tension, generalising recent results in arXiv:2011.02885.