Equivariant Verlinde Formula from Fivebranes and Vortices

作     者：Gukov, Sergei Pei, Du 

作者机构：CALTECH Walter Burke Inst Theoret Phys Pasadena CA 91125 USA Max Planck Inst Math Vivatsgasse 7 D-53111 Bonn Germany 

出 版 物：《COMMUNICATIONS IN MATHEMATICAL PHYSICS》 (数理物理通讯)

年 卷 期：2017年第355卷第1期

页      面：1-50页

核心收录：

学科分类：07[理学] 070201[理学-理论物理] 0702[理学-物理学] 

基　　金：DOE [DE-SC0011632] NSF [DMS 1107452, 1107263, 1107367] Walter Burke Institute for Theoretical Physics 

主　　题：CHERN-Simons gauge theory SUPERSYMMETRY (Physics) STRING theory MANIFOLDS (Mathematics) PARTITION functions DIRAC operators 

摘      要：We study complex Chern-Simons theory on a Seifert manifold M (3) by embedding it into string theory. We show that complex Chern-Simons theory on M (3) is equivalent to a topologically twisted supersymmetric theory and its partition function can be naturally regularized by turning on a mass parameter. We find that the dimensional reduction of this theory to 2d gives the low energy dynamics of vortices in four-dimensional gauge theory, the fact apparently overlooked in the vortex literature. We also generalize the relations between (1) the Verlinde algebra, (2) quantum cohomology of the Grassmannian, (3) Chern-Simons theory on and (4) index of a spin (c) Dirac operator on the moduli space of flat connections to a new set of relations between (1) the equivariant Verlinde algebra for a complex group, (2) the equivariant quantum K-theory of the vortex moduli space, (3) complex Chern-Simons theory on and (4) the equivariant index of a spin (c) Dirac operator on the moduli space of Higgs bundles.