Modular and duality properties of surface operators in N=2* gauge theories

Abstract

We calculate the instanton partition function of the four-dimensional N=2* SU(N) gauge theory in the presence of a generic surface operator, using equivariant localization. By analyzing the constraints that arise from S-duality, we show that the effective twisted superpotential, which governs the infrared dynamics of the two-dimensional theory on the surface operator, satisfies a modular anomaly equation. Exploiting the localization results, we solve this equation in terms of elliptic and quasi-modular forms which resum all non-perturbative corrections. We also show that our results, derived for monodromy defects in the four-dimensional theory, match the effective twisted superpotential describing the infrared properties of certain two-dimensional sigma models coupled either to pure N=2 or to N=2* gauge theories.

51 pages, v3: references added, typos fixed, footnote added, some small changes in the text, appendix B streamlined. Matches the published version

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Cited by in corpus (12)

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• A slow review of the AGT correspondence
• Surface operators, chiral rings, and localization in N=2 gauge theories
• Bands and gaps in Nekrasov partition function
• Surface defects, flavored modular differential equations and modularity
• Surface operators in 5d gauge theories and duality relations
• Surface operators, dual quivers and contours
• Surface Defects from Fractional Branes -- I
• Chiral rings for surface operators in 4d and 5d SQCD
• Modular properties of surface operators in N=2 SQCD
• Painlevé Kernels and Surface Defects at Strong Coupling