Factorization of the 3d superconformal index with an adjoint matter

Understand

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.