Index computation for 3d Chern-Simons matter theory: test of Seiberg-like duality

TL;DR

The paper tests Seiberg-like dualities in three-dimensional N=2 Chern-Simons matter theories by computing the exact superconformal index for dual pairs with gauge groups U(N), Sp(2N), and O(N) and fundamental matter. Using localization on $S^1\times S^2$, the authors sum over monopole fluxes and holonomies and incorporate CS terms, deriving explicit index expressions for unitary, symplectic, and orthogonal cases. They demonstrate precise agreement between electric-magnetic duals up to high orders in the $p$-$q$ expansion, validating the proposed dualities and highlighting the roles of chiral ring and monopole operators. The results extend evidence for 3d Seiberg-like dualities and showcase the index as a robust diagnostic tool that can be applied to other dualities and potentially yield analytic proofs.

Abstract

We work out the superconformal index for N=2 supersymmetric Chern-Simons matter theories exhibiting Seiberg-like dualities proposed by Giveon and Kutasov. We consider $U(N)/Sp(2N)/O(N)$ gauge theories of QCD type and find the perfect agreements for proposed dual pairs.