Is toric duality a Seiberg-like duality in (2 + 1)-d ?

Abstract

Abstract: We show that not all (2 + 1) dimensional toric phases are Seiberg-like duals. Particularly, we work out superconformal indices for the toric phases of Fanos C3, C5 and B2. We find that the indices for the two toric phases of Fano B2 do not match, which implies that they are not Seiberg-like duals. We also take the route of acting Seiberg-like duality transformation on toric quiver Chern-Simons theories to obtain dual quivers. We study two examples and show that Seiberg-like dual quivers are not always toric quivers.