The 1/2 BPS 't Hooft loops in N=4 SYM as instantons in 2d Yang-Mills

TL;DR

The authors formulate a localization-based approach to 1/2 BPS t' Hooft loops in N=4 SYM, showing that the presence of such magnetic operators reduces 4d computations to the unstable instanton sectors of 2d YM on S^2. They establish and test a precise conjecture that the 4d vevs and Wilson–'t Hooft correlators are captured by 2d YM instanton contributions, yielding exact results that are consistent with S-duality, including a dual Gaussian matrix model for vevs and explicit correlators in the fundamental representation. This work deepens the understanding of nonperturbative observables in N=4 SYM and illustrates a concrete bridge between 4d localization and 2d Yang-Mills theory. It also clarifies when monopole bubbling can be neglected and outlines extensions to more general groups, representations, and theta angles.

Abstract

We extend the recent conjecture on the relation between a certain 1/8 BPS subsector of 4d N=4 SYM on S^2 and 2d Yang-Mills theory by turning on circular 1/2 BPS 't Hooft operators linked with S^2. We show that localization predicts that these 't Hooft operators and their correlation functions with Wilson operators on S^2 are captured by instanton contributions to the partition function of the 2d Yang-Mills theory. Based on this prediction, we compute explicitly correlation functions involving the 't Hooft operator, and observe precise agreement with S-duality predictions.