A bstract We investigate an N = 4 U N k × U N + M ? k $$ mathcal{N} = 4;mathrm{U}{(N)}_kimes mathrm{U}{left(N+Might)}_{-k} $$ Chern-Simons theory coupled to one bifundamental hypermultiplet by employing its partition function, which is given by 2 N + M dimensional integration via localization. Surprisingly, by performing the integration explicitly we find that the partition function completely factorizes into that of the pure Chern-Simons theory for two gauge groups and an analogous contribution for the bifundamental hypermultiplet. Using the factorized form of the partition function we argue the level/rank duality, which is also expected from the Hanany-Witten transition in the type IIB brane realization. We also present the all order ’t Hooft expansion of the partition function and comment on the connection to the higher-spin theory.
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机译：Bstract我们调查n = 4 u n k×u n + m？ k $$ mathcal {n} = 4 ; mathrm {u} {（n）} _ k times mathrm {u} { left（n + m light）} _ { - k} $$ chern- 通过采用其分区函数耦合到一个横向高温池的西蒙斯理论，其通过定位由2 n + m维集成给出。 令人惊讶的是，通过明确地进行整合，我们发现分区功能完全分解为两个规格组的纯Chern-Simons理论和对平均过高潜力量的类似贡献。 使用分区功能的分解形式，我们争论级别/等级二元性，这也是IIB型Brane实现中的Hanany Witting转换。 我们还介绍了分区功能的所有订单T Hooft扩展，并对与较高自旋理论的连接进行了评论。
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