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

Satoshi Nawata

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

High Energy Physics - Theory 2017-04-25 v4 Algebraic Geometry Representation Theory

Authors: Satoshi Nawata

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 $\mathcal{N}=2^*$ 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.

Keywords

supersymmetric gauge theory superconformal field theories gauge theory and string theory

Cite

@article{arxiv.1408.4132,
  title  = {Givental J-functions, Quantum integrable systems, AGT relation with surface operator},
  author = {Satoshi Nawata},
  journal= {arXiv preprint arXiv:1408.4132},
  year   = {2017}
}

Comments

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

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

Abstract

Keywords

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