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

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.

38 pages; v2: references added, typos fixed

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Cited by in corpus (30)

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• Quantum black holes, localization and the topological string
• Exact Results for 't Hooft Loops in Gauge Theories on S^4
• On the instantons and the hypermultiplet mass of N=2* super Yang-Mills on S^4
• A note on perturbation series in supersymmetric gauge theories
• New Modular Invariants in $\mathcal{N}=4$ Super-Yang-Mills Theory
• Exact results for Wilson loops in arbitrary representations
• Line Operator Index on S1 $\times$ S3
• Line Defects, Tropicalization, and Multi-Centered Quiver Quantum Mechanics
• S-duality, 't Hooft operators and the operator product expansion
• Resummation and S-duality in N=4 SYM
• Exact probes of orientifolds
• Free energy and defect $C$-theorem in free scalar theory
• 't Hooft Operators in Gauge Theory from Toda CFT
• Classifying Superconformal Defects in Diverse Dimensions Part I: Superconformal Lines
• Holographic Higgs Phases
• On the Global Structure of Deformed Yang-Mills Theory and QCD(adj) on ${\mathbb{R}}^3\times {\mathbb{S}}^1$
• Resumming perturbative series in the presence of monopole bubbling effects
• One Monopole with k Singularities
• Instanton effects in correlation functions on the light-cone
• Quantum 't Hooft loops of SYM N=4 as instantons of YM_2 in dual groups SU(N) and SU(N)/Z_N
• Quantum entropy of supersymmetric black holes
• Superselection, Boundary Algebras and Duality in Gauge Theories
• S-duality of boundary lines in $\mathcal{N}=4$ SYM theories and supersymmetric indices
• More on 't Hooft loops in N=4 SYM
• S-duality transformation of $\mathcal{N}$ $=4$ SYM theory at the operator level
• S-duality and loop operators in canonical formalism