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

Abstract

I will talk about 4d 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 N=2* theory, a full surface operator can be described as the 4d gauge theory coupled to a 2d 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, I will show the validity of the orbifold method in one-loop computations when a full surface operator is inserted, and the form of the structure constants with a semi-degenerate field in SL(N,R) WZNW model is predicted from one-loop determinants.