ABCD of 't Hooft operators

TL;DR

This paper uses supersymmetric localization to compute expectation values of half-BPS 't Hooft line operators in various 4D $ ext{N}=2$ gauge theories on a deformed space, incorporating non-perturbative monopole effects.

Contribution

It introduces a novel method combining brane constructions and supersymmetric indices to evaluate 't Hooft operator expectation values in $ ext{N}=2$ theories with non-perturbative monopole screening.

Findings

Explicit formulas for 't Hooft operator expectation values in $U(N)$, $SO(N)$, and $USp(N)$ theories.

Inclusion of monopole screening effects via supersymmetric quantum mechanics indices.

Application of brane and orientifold setups to gauge theory computations.

Abstract

We compute by supersymmetric localization the expectation values of half-BPS 't Hooft line operators in $\mathcal{N}=2$ $U(N)$, $SO(N)$ and $USp(N)$ gauge theories on $S^1 \times \mathbb{R}^3$ with an $\Omega$-deformation. We evaluate the non-perturbative contributions due to monopole screening by calculating the supersymmetric indices of the corresponding supersymmetric quantum mechanics, which we obtain by realizing the gauge theories and the 't Hooft operators using branes and orientifolds in type II string theories.