Complete factorization in minimal N= 4 Chern-Simons-matter theory

Abstract

We investigate an N=4U(N)k×U(N+M)−k Chern-Simons theory coupled to one bifundamental hypermultiplet by employing its partition function, which is given by 2N + 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.