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Quantum ’t Hooft operators and \(S\)-duality in \(N=4\) super Yang-Mills. (English) Zbl 1200.81109

Summary: We provide a quantum path integral definition of an ’t Hooft loop operator, which inserts a point-like 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.

MSC:

81T13 Yang-Mills and other gauge theories in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
81S40 Path integrals in quantum mechanics
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
81V10 Electromagnetic interaction; quantum electrodynamics
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