Factorization of the 3d superconformal index with an adjoint matter

TL;DR

This paper develops a method to factorize the 3d superconformal index for certain gauge theories, enabling proof of dualities and analysis of monopole operators, with extensive numerical validation.

Contribution

It introduces a factorization approach for the 3d superconformal index in theories with adjoint matter, facilitating proof of Seiberg-like dualities and analysis of monopole operators.

Findings

Factorization of the 3d superconformal index for N=2 U(N_c) theories with adjoint matter.

Proof of Seiberg-like duality at the index level for these theories.

Numerical checks confirming the derived combinatorial identities.

Abstract

We work out the factorization of the 3d superconformal index for N = 2 $U(N_c)$ gauge theory withone adjoint chiral multiplet as well as $N_f$ fundamental, $N_a$ anti-fundamental chiral multiplets. Using the factorization,one can prove the Seiberg-like duality for N = 4 $U(N_c)$ theory with $N_f$ hypermultiplets at the index level. We explicitlyshow that monopole operators violating unitarity bound in a bad theory are mapped to free hypermultiplets in the dual side. For N = 2 $U(N_c)$ theory with one adjoint matter $X$, $N_f$ fundamental, $N_a$ anti-fundamental chiral multiplets with superpotential $W = tr X^{n+1}$, 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.