Reducing the 4d index to the S3 partition function
Reducing the 4d index to the S3 partition function
复制标题
将 4d 索引简化为 S3 分区函数
DOI：
--
复制
发表时间：
2011
期刊：
影响因子：
--
通讯作者：
Wenbin Yan
中科院分区：
文献类型：
--
作者：
Abhijit Gadde;Wenbin Yan
摘要 4d 规范理论的超共形指数是通过 S3 × S1 上超对称路径积分的局部化产生的矩阵积分来计算的。当圆的半径趋于零时，很自然地期望 4d 路径积分成为 S3 上降维规范理论的配分函数。我们证明情况确实如此，并从计算超共形指数的矩阵积分中恢复 Kapustin、Willett 和 Yaakov 的矩阵积分。值得注意的是，“父”4d 理论的超共形指数可以被认为是 3d 配分函数的 q 变形。
A bstractThe superconformal index of a 4d gauge theory is computed by a matrix integral arising from localization of the supersymmetric path integral on S3 × S1. As the radius of the circle goes to zero, it is natural to expect that the 4d path integral becomes the partition function of dimensionally reduced gauge theory on S3. We show that this is indeed the case and recover the matrix integral of Kapustin, Willett and Yaakov from the matrix integral that computes the superconformal index. Remarkably, the superconformal index of the “parent” 4d theory can be thought of as the q-deformation of the 3d partition function.