On the structure of non-planar strong coupling corrections to correlators of BPS Wilson loops and chiral primary operators

TL;DR

This paper analyzes the structure of non-planar strong coupling corrections to correlators involving BPS Wilson loops and chiral primary operators in ${ m extbf{N}=4}$ SYM and ABJM theories, revealing resummation patterns in their expansions.

Contribution

It uncovers the specific resummation structures of non-planar corrections at strong coupling for Wilson loop correlators, extending understanding of their large 't Hooft coupling behavior.

Findings

Correlators expand in powers of g_s^2/T^2, with leading terms summing into simple functions.

Leading strong coupling terms in correlators form a square root function of g_s^2/T^2.

Similar expansion patterns are observed for coincident Wilson loops in ABJM theory.

Abstract

Starting with some known localization (matrix model) representations for correlators involving 1/2 BPS circular Wilson loop $\cal W$ in ${\cal N}=4$ SYM theory we work out their $1/N$ expansions in the limit of large 't Hooft coupling $\lambda$. Motivated by a possibility of eventual matching to higher genus corrections in dual string theory we follow arXiv:2007.08512 and express the result in terms of the string coupling $g_{\rm s} \sim g^2_{\rm YM} \sim \lambda/N$ and string tension $T\sim \sqrt \lambda$. Keeping only the leading in $1/T$ term at each order in $g_{\rm s} $ we observe that while the expansion of $\langle {\cal W} \rangle$ is a series in $g^2_{\rm s} /T$, the correlator of the Wilson loop with chiral primary operators ${\cal O}_J $ has expansion in powers of $g^2_{\rm s}/T^2$. Like in the case of $\langle {\cal W} \rangle$ where these leading terms are known to resum into an exponential of a "one-handle" contribution $\sim g^2_{\rm s} /T$, the leading strong coupling terms in $\langle {\cal W}\, {\cal O}_J \rangle$ sum up to a simple square root function of $g^2_{\rm s}/T^2$. Analogous expansions in powers of $g^2_{\rm s}/T$ are found for correlators of several coincident Wilson loops and they again have a simple resummed form. We also find similar expansions for correlators of coincident 1/2 BPS Wilson loops in the ABJM theory.