S-duality, 't Hooft operators and the operator product expansion

TL;DR

The paper tests S-duality in N=4 SYM for arbitrary gauge groups by computing the OPEs of circular loop operators with chiral primaries: the 't Hooft loop is treated perturbatively at weak coupling, while the dual Wilson loop is analyzed at strong coupling via a matrix-model formulation. The authors derive explicit OPE coefficients and scaling weights for both loop operators and show that they match under the S-duality map between G and its dual ^LG, including the invariance of two- and three-point functions of chiral primaries and the relation $b_Δ={}^{L}c_Δ$. This provides a quantitative demonstration that S-duality extends to correlation functions and OPE data, beyond mere expectation values, for general gauge groups. The matrix-model methods and background-field path integral together establish a robust framework for testing nonperturbative dualities in gauge theories.

Abstract

We study S-duality in N=4 super Yang-Mills with an arbitrary gauge group by determining the operator product expansion of the circular BPS Wilson and 't Hooft loop operators. The coefficients in the expansion of an 't Hooft loop operator for chiral primary operators and the stress-energy tensor are calculated in perturbation theory using the quantum path-integral definition of the 't Hooft operator recently proposed. The corresponding operator product coefficients for the dual Wilson loop operator are determined in the strong coupling expansion. The results for the 't Hooft operator in the weak coupling expansion exactly reproduce those for the dual Wilson loop operator in the strong coupling expansion, thereby demonstrating the quantitative prediction of S-duality for these observables.