Givental J-functions, Quantum integrable systems, AGT relation with surface operator

Abstract

We study 4d $\mathcal{N}=2$ gauge theories with a co-dimension two full surface operator, which exhibit a fascinating interplay of supersymmetric gauge theories, equivariant Gromov-Witten theory and geometric representation theory. For pure Yang-Mills and $\mathcal{N}=2^{\ast }$ theory, we describe a full surface operator as the 4d gauge theory coupled to a 2d $\mathcal{N}=(2,2)$ gauge theory. By supersymmetric localizations, we present the exact partition functions of both 4d and 2d theories which satisfy integrable equations. In addition, the form of the structure constants with a semi-degenerate field in SL(N,R) WZNW model is predicted from one-loop determinants of 4d gauge theories with a full surface operator via the AGT relation.

45 pages, 6 figures, 1 table; result in Appendix A has been obtained with Antonio Sciarappa and Junya Yagi; v2, v3, v4 minor corrections and reference added

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• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• Higgs branch localization in three dimensions
• M2-brane surface operators and gauge theory dualities in Toda
• Higgs branch localization of 3d N=2 theories
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Cited by in corpus (5)

• Defects and Quantum Seiberg-Witten Geometry
• Surface Operators and Separation of Variables
• Orbifolds, Defects and Sphere Partition Function
• Series Solutions of the Non-Stationary Heun Equation
• Les Houches lectures on non-perturbative Seiberg-Witten geometry