’t Hooft Operators in Gauge Theory from Toda CFT

Abstract

We construct loop operators in two dimensional Toda CFT and calculate with them the exact expectation value of certain supersymmetric 't Hooft and dyonic loop operators in four dimensional $ \mathcal{N} = 2 $ gauge theories with SU(N) gauge group. Explicit formulae for 't Hooft and dyonic operators in $ \mathcal{N} = 2 * $ and $ \mathcal{N} = 2 $ conformal SQCD with SU(N) gauge group are presented. We also briefly speculate on the Toda CFT realization of arbitrary loop operators in these gauge theories in terms of topological web operators in Toda CFT.