Exact Results for 't Hooft Loops in Gauge Theories on S^4

TL;DR

This paper computes exact expectation values of 't Hooft loops in N=2 supersymmetric gauge theories on S^4 using localization, capturing all quantum corrections and confirming predictions from Liouville/Toda CFT.

Contribution

It provides the first exact localization-based calculation of 't Hooft loops on S^4, including perturbative and non-perturbative effects, and confirms duality predictions.

Findings

Exact 't Hooft loop expectation values obtained.

Results match predictions from Liouville/Toda conformal field theory.

Non-perturbative effects from instantons and monopoles are included.

Abstract

The path integral of a general N=2 supersymmetric gauge theory on S^4 is exactly evaluated in the presence of a supersymmetric 't Hooft loop operator. The result we find - obtained using localization techniques - captures all perturbative quantum corrections as well as non-perturbative effects due to instantons and monopoles, which are supported at the north pole, south pole and equator of S^4. As a by-product, our gauge theory calculations successfully confirm the predictions made for 't Hooft loops obtained from the calculation of topological defect correlators in Liouville/Toda conformal field theory.