A note on 't Hooft-line defect integrated correlators in $\mathcal{N}=4$ supersymmetric Yang-Mills theory

TL;DR

This paper derives the perturbative expansion of integrated correlators in $ ext{N}=4$ supersymmetric Yang-Mills theory with 't Hooft-line defects, using a lattice sum approach and supersymmetric localization for $SU(2)$.

Contribution

It introduces a novel method to compute integrated correlators with 't Hooft-line defects for higher-rank gauge groups where localization is not available.

Findings

Matching with localization results for $SU(2)$

Perturbative expansion for higher-rank gauge groups

Use of automorphic properties in lattice sum

Abstract

We derive the perturbative expansion of a particular integrated correlator of two superconformal primary operators in the stress tensor multiplet of $\mathcal{N}=4$ supersymmetric $SU(N)$ Yang-Mills theory in the presence of a half-BPS 't Hooft-line defect. The calculation is based on a recently derived expression for this physical observable in terms of a two-dimensional lattice sum with manifest automorphic properties under the electromagnetic duality group. When the gauge group is $SU(2)$, this analysis matches with the presented supersymmetric localisation approach while for higher-rank gauge groups, where no alternative formulation is available, the methods introduced prove to be crucial in obtaining the perturbative expansion of integrated correlators for 't Hooft-line defects.