Tests of Seiberg-like Duality in Three Dimensions

TL;DR

This paper uses localization to verify Seiberg-like dualities in 3D supersymmetric gauge theories, confirming their validity at the level of partition functions and exploring their connections to level-rank duality and M2 brane theories.

Contribution

It demonstrates the validity of Giveon-Kutasov duality through partition function comparisons and clarifies its relation to level-rank duality and fractional M2 brane theories.

Findings

Seiberg-like duality holds at the partition function level.

Relation between Giveon-Kutasov duality and level-rank duality established.

Confirmation of decoupled free sectors in N=4 theories via monopole operators.

Abstract

We use localization techniques to study several duality proposals for supersymmetric gauge theories in three dimensions reminiscent of Seiberg duality. We compare the partition functions of dual theories deformed by real mass terms and FI parameters. We find that Seiberg-like duality for N=3 Chern-Simons gauge theories proposed by Giveon and Kutasov holds on the level of partition functions and is closely related to level-rank duality in pure Chern-Simons theory. We also clarify the relationship between the Giveon-Kutasov duality and a duality in theories of fractional M2 branes and propose a generalization of the latter. Our analysis also confirms previously known results concerning decoupled free sectors in N=4 gauge theories realized by monopole operators.