论文标题
镜头分区功能，五角大楼身份和星际关系
Lens partition function, pentagon identity and star-triangle relation
论文作者
论文摘要
我们通过使用量规/ybe通信来研究$ s^3/\ mathbb {z} _r $上的$ \ mathcal n = 2 $ supersymmetric duage双重理论的三维镜头分区函数。这种对应关系将超对称量规理论与统计力学的准确解决模型联系起来。三维超对称双重理论的分区函数的平等性可以写为双曲超单几何函数的积分身份。我们获得了这样一个积分的身份，可以写为ISING类型集成模型的Star-Triangle关系，以及五角大楼的积分身份。后者代表了三角剖分3个manifolds的基本2-3 pachner移动。我们的积分身份的一种特殊情况可用于证明$ u_q（osp（1 | 2））$的自动连续系列的clebsch-gordan系数的正交性和完整性关系。
We study the three-dimensional lens partition function for $\mathcal N=2$ supersymmetric gauge dual theories on $S^3/\mathbb{Z}_r$ by using the gauge/YBE correspondence. This correspondence relates supersymmetric gauge theories to exactly solvable models of statistical mechanics. The equality of partition functions for the three-dimensional supersymmetric dual theories can be written as an integral identity for hyperbolic hypergeometric functions. We obtain such an integral identity which can be written as the star-triangle relation for Ising type integrable models and as the integral pentagon identity. The latter represents the basic 2-3 Pachner move for triangulated 3-manifolds. A special case of our integral identity can be used for proving orthogonality and completeness relation of the Clebsch-Gordan coefficients for the self-dual continuous series of $U_q(osp(1|2))$.
