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

## TL;DR

This paper analyzes an N=4 Chern-Simons-matter theory, revealing a complete factorization of its partition function into simpler components, and discusses implications for dualities and higher-spin theories.

## Contribution

It explicitly computes the partition function, demonstrating its full factorization and supporting the level/rank duality in the theory.

## Key findings

- Partition function fully factorizes into pure Chern-Simons parts and hypermultiplet contributions.
- Supports the level/rank duality via the factorized form.
- Provides the all-order 't Hooft expansion and discusses higher-spin connections.

## Abstract

We investigate an N=4 U(N)_k x 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.