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 mathcal{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 mathcal{N} = 4 gauge theories realized by monopole operators.
Highlights
Beautiful example of this phenomenon is Seiberg duality of N = 1 gauge theories in four dimensions [1]
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 levelrank duality in pure Chern-Simons theory
The duality proposals in three dimensions are based on brane constructions in type IIB string theory of the type introduced by Hanany and Witten in [6]
Summary
The low energy action on an infinite flat type IIB d-brane is a maximally supersymmetric gauge theory in d+1 dimensions. If the Chern-Simons couplings for some or all simple gauge group factors are absent and the integrand does not decay in all directions in the eigenvalue space, the integral cannot be defined in this way and one has to interpret the divergence. Gaiotto and Witten [5] formulated a seemingly different necessary condition for the naive R-symmetry to be part of the stress-energy tensor multiplet They required that the dimensions of all BPS monopole operators computed assuming the naive R-symmetry be greater or equal to 1/2 (this is required by the unitarity of the theory). This gives the following condition for every simple factor G of the gauge group:. The calculation for large rank gauge groups becomes increasingly numerically demanding and only low rank results are provided
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