Complete factorization in minimal N=4 $$ \mathcal{N}=4 $$ Chern-Simons-matter theory

Abstract

Abstract We investigate an N=4UNk×UN+M−k $$ \mathcal{N} = 4\;\mathrm{U}{(N)}_k\times \mathrm{U}{\left(N+M\right)}_{-k} $$ 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.

Keywords

• Chern-Simons Theories
• Duality in Gauge Field Theories
• Matrix Models
• Supersymmetric Gauge Theory