Partition function (quantum field theory)

S-duality

Quantum mechanics

Theoretical physics

Pure mathematics

Mathematical physics

Relationship between string theory and quantum field theory

Seiberg duality

Magnetic monopole

Quantum gravity

Particle physics

Literature

Supersymmetric gauge theory

Rank (graph theory)

Duality (order theory)

Gauge theory

Gauge anomaly

Physics

Mathematics

Quantum electrodynamics

Mathematical analysis

Partition (number theory)

Quantum

Combinatorics

Dual (grammatical number)

Generalization

Journal of High Energy Physics

A bstract 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 $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 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 $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 4 gauge theories realized by monopole operators.

Tests of Seiberg-like dualities in three dimensions