Equivariant Verlinde Algebra from Superconformal Index and Argyres–Seiberg Duality
Equivariant Verlinde Algebra from Superconformal Index and Argyres–Seiberg Duality
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DOI：
10.1007/s00220-017-3074-8
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发表时间：
2016-05
影响因子：
2.4
通讯作者：
S. Gukov;Du Pei;Wenbin Yan;Ke Ye
中科院分区：
文献类型：
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作者：
S. Gukov;Du Pei;Wenbin Yan;Ke Ye
本文证明了两个看似不同的二维TQFT之间的等价性：一个来自于经典理论的“库仑分支指数”，另一个来自于“等变Verlinde公式”，即复Chern-Simons理论的等价配分函数，我们首先利用M-理论几何导出了这一等价性，并证明了出现在两侧的规范群自然是G及其Langlands对偶。当G不是单连通时，我们给出了一个计算G的指数的方法，它是对具有非平凡背景t Hooft通量的G的指数的求和，其中G是G的泛覆盖。然后我们显式检查库仑指数与orSO（3）的等变Verlinde公式之间的关系。最后，作为这个新发现的关系的一个应用，我们考虑了GisSU（N）或PSU（N）的更一般的情形，并证明了等变Verlinde代数可以通过（广义）Argyres-Seiberg对偶由场论导出.我们还附上了一个Mathematica笔记本，可以用来计算SU（3）等变Verlinde系数。
In this paper, we show the equivalence between two seemingly distinct 2d TQFTs: one comes from the “Coulomb branch index” of the classtheoryon, the other is the“equivariant Verlinde formula”, or equivalently partition function ofcomplex Chern–Simons theory on. We first derive this equivalence using the M-theory geometry and show that the gauge groups appearing on the two sides are naturallyGand its Langlands dual. WhenGis not simply-connected, we provide a recipe of computing the index ofas summation over the indices ofwith non-trivial background ’t Hooft fluxes, whereis the universal cover ofG. Then we check explicitly this relation between the Coulomb index and the equivariant Verlinde formula fororSO(3). In the end, as an application of this newly found relation, we consider the more general case whereGisSU(N) orPSU(N) and show that equivariant Verlinde algebra can be derived using field theory via (generalized) Argyres–Seiberg duality. We also attach a Mathematica notebook that can be used to compute theSU(3) equivariant Verlinde coefficients.