Quantum 't Hooft operators and S-duality in N=4 super Yang-Mills

TL;DR

The paper defines a quantum path-integral 't Hooft loop in N=4 SYM and computes its circular-loop expectation value at weak coupling for arbitrary gauge group G, including the necessary adjoint-orbit measure. Using Pestun localization, it then evaluates the dual circular Wilson loop in the S-dual theory ${}^L G$ at strong coupling, obtaining a matching leading exponential. The authors demonstrate, to next-to-leading order, that the weak-coupling result for the 't Hooft loop exactly reproduces the strong-coupling expansion of the dual Wilson loop, providing a quantitative test of S-duality for correlation functions in ${ m N}=4$ SYM. They further identify monopole screening as the origin of subleading exponential corrections and propose extensions to localization for monopole operators and to other ${ m N}=2$ theories, highlighting broader implications for dualities and holography.

Abstract

We provide a quantum path integral definition of an 't Hooft loop operator, which inserts a pointlike monopole in a four dimensional gauge theory. We explicitly compute the expectation value of the circular 't Hooft operators in N=4 super Yang-Mills with arbitrary gauge group G up to next to leading order in perturbation theory. We also compute in the strong coupling expansion the expectation value of the circular Wilson loop operators. The result of the computation of an 't Hooft loop operator in the weak coupling expansion exactly reproduces the strong coupling result of the conjectured dual Wilson loop operator under the action of S-duality. This paper demonstrates - for the first time - that correlation functions in N=4 super Yang-Mills admit the action of S-duality.