FROM 4d SUPERCONFORMAL INDICES TO 3d PARTITION FUNCTIONS
FROM 4d SUPERCONFORMAL INDICES TO 3d PARTITION FUNCTIONS
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从 4d 超共形索引到 3d 配分函数
DOI：
10.1016/j.physletb.2011.09.007
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发表时间：
2011
影响因子：
4.4
通讯作者：
G. Vartanov
中科院分区：
文献类型：
--
作者：
F. Dolan;V. Spiridonov;G. Vartanov
最近，Jafferis、Hama、Hosomichi和Lee提出了三维场理论中配分函数的精确公式。这些函数用特定的q-超几何积分来表示，其关键构件是双正弦函数(或双曲伽马函数)。由第二作者发现的椭圆超几何积分定义了4D超共形指数。利用它们在双曲水平上的约化，我们描述了将4D超共形指数降为3D配分函数的一般方案，这意味着从SYM理论的4dN=1对偶得到SYM和CS理论的3dN=2超对称对偶是一种有效的方法。作为一个例子，我们显式地考虑了具有反对称张量物质的SP(2N)规范群的3dN=2 SYM和CS理论的对偶模式。
An exact formula for partition functions in 3d field theories was recently suggested by Jafferis, and Hama, Hosomichi, and Lee. These functions are expressed in terms of specific q-hypergeometric integrals whose key building block is the double sine function (or the hyperbolic gamma function). Elliptic hypergeometric integrals, discovered by the second author, define 4d superconformal indices. Using their reduction to the hyperbolic level, we describe a general scheme of reducing 4d superconformal indices to 3d partition functions which imply an efficient way of getting 3dN=2 supersymmetric dualities for both SYM and CS theories from the “parent” 4dN=1 dualities for SYM theories. As an example, we consider explicitly the duality pattern for 3dN=2 SYM and CS theories with SP(2N) gauge group with the antisymmetric tensor matter.