Factorization of the 3d superconformal index with an adjoint matter

Abstract

Abstract: We work out the factorization of the 3d superconformal index for N = 2 U(Nc) gauge theory with one adjoint chiral multiplet as well as Nf fundamental, Na anti-fundamental chiral multiplets. Using the factorization, one can prove the Seiberg-like duality for N=4 U(Nc) theory with Nf hypermultiplets at the index level. We explicitly show that monopole operators violating unitarity bound in a bad theory are mapped to free hypermultiplets in the dual side. For N=2 U(Nc) theory with one adjoint matter X, Nf fundamental, Na anti-fundamental chiral multiplets with superpotential W = trXn+1, we work out Seiberg-like duality for this theory. The index computation provides combinatorial identities for a dual pair, which we carry out intensive numerical checks.