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

TL;DR

This paper investigates S-duality in N=4 super Yang-Mills by calculating operator product expansions of Wilson and 't Hooft loops, confirming duality predictions through perturbative and strong coupling analyses.

Contribution

It provides explicit calculations of OPE coefficients for 't Hooft and Wilson loops, demonstrating quantitative S-duality predictions in N=4 super Yang-Mills.

Findings

Weak coupling 't Hooft operator coefficients match strong coupling Wilson loop coefficients.

Perturbative calculations confirm S-duality predictions.

Results support the operator product expansion framework 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.