Elliptic hypergeometric sum/integral transformations and supersymmetric lens index
Elliptic hypergeometric sum/integral transformations and supersymmetric lens index
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DOI：
10.3842/sigma.2018.013
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发表时间：
2016-02
影响因子：
0.9
通讯作者：
A. P. Kels;M. Yamazaki
中科院分区：
文献类型：
--
作者：
A. P. Kels;M. Yamazaki
本文证明了一对与$A_n$和$BC_n$根系相关的多元椭圆超几何和\斜线积分的变换公式，推广了Rains以前得到的公式.的总和/积分表示的透镜椭圆伽马函数，椭圆伽马函数的推广，取决于一个额外的整数变量，以及一个复杂的变量和两个椭圆诺姆。作为我们结果的应用，我们证明了一对四维$N =1$超对称规范理论的S^1 × S^3/Z r$超对称指标之间的一个等式，其中规范群为SU（n+1）$和Sp（2n）$，它们之间存在Seiberg对偶关系.这提供了迄今为止已知的对塞贝格对偶性的最精细的检验之一。作为$A_n$积分的另一个应用，我们证明了第二作者以前给出的一个二维统计力学可积格点模型的星-星关系。
We prove a pair of transformation formulas for multivariate elliptic hypergeometric sum\slash integrals associated to the $A_n$ and $BC_n$ root systems, generalising the formulas previously obtained by Rains. The sum/integrals are expressed in terms of the lens elliptic gamma function, a generalisation of the elliptic gamma function that depends on an additional integer variable, as well as a complex variable and two elliptic nomes. As an application of our results, we prove an equality between $S^1\times S^3/\mathbb{Z}_r$ supersymmetric indices, for a pair of four-dimensional $\mathcal{N}=1$ supersymmetric gauge theories related by Seiberg duality, with gauge groups $SU(n+1)$ and $Sp(2n)$. This provides one of the most elaborate checks of the Seiberg duality known to date. As another application of the $A_n$ integral, we prove a star-star relation for a two-dimensional integrable lattice model of statistical mechanics, previously given by the second author.