Quantum 't Hooft loops of SYM N=4 as instantons of YM_2 in dual groups SU(N) and SU(N)/Z_N

TL;DR

This paper explores the relationship between 1/2 BPS 't Hooft operators in 4d N=4 SYM and instantons in 2d Yang-Mills theory, focusing on non-self-dual groups and non-minimal representations, extending previous conjectures.

Contribution

It extends the conjectured relation between 't Hooft operators and YM_2 instantons to the cases of SU(N) and SU(N)/Z_N groups with various representations.

Findings

Identifies peculiarities for non-self-dual groups.

Analyzes effects of non-minimal representations.

Provides insights into dual group representations.

Abstract

A relation between circular 1/2 BPS 't Hooft operators in 4d N=4 SYM and instantonic solutions in 2d Yang-Mills theory (YM_2) has recently been conjectured. Localization indeed predicts that those 't Hooft operators in a theory with gauge group G are captured by instanton contributions to the partition function of YM_2, belonging to representations of the dual group ^LG. This conjecture has been tested in the case G=U(N)=^LG and for fundamental representations. In this paper we examine this conjecture in the case of the groups G=SU(N) and ^LG=SU(N)/Z_N and loops in different representations. Peculiarities when groups are not self-dual and representations not "minimal" are pointed out.