N=2 gauge theories, instanton moduli spaces and geometric representation theory

[摘要] We survey some of the AGT relations between N = 2 gauge theories in four dimensions and geometric representations of symmetry algebras of two-dimensional conformal field theory on the equivariant cohomology of their instanton moduli spaces. We treat the cases of gauge theories on both flat space and ALE spaces in some detail, and with emphasis on the implications arising from embedding them into supersymmetric theories in six dimensions. Along the way we construct new toric noncommutative ALE spaces using the general theory of complex algebraic deformations of toric varieties, and indicate how to generalize the construction of instanton moduli spaces. We also compute the equivariant partition functions of topologically twisted six-dimensional Yang-Mills theory with maximal super symmetry in a general Omega-background, and use the construction to obtain novel reductions to theories in four dimensions. (C) 2015 Elsevier B.V. All rights reserved.

[发布日期] 2016-11-01

[效力级别]  Proceedings Paper

[关键词] Instanton counting;Supersymmetric gauge theories;AGT correspondence;Representation theory;Conformal field theory