Classification of monopole deformed 3d $\mathcal{N}=2$ Seiberg-like duality with an adjoint matter

Abstract: We propose a new 3d $\mathcal{N}=2$ Seiberg-like duality of adjoint SQCD(Kim-Park duality) with linear monopole superpotential terms which encompasses known monopole deformed Kim-Park dualities. Equipped with this, we classify all the monopole deformed Kim--Park dualities up to quadratic powers of monopole deformations, and find all are equivalent either to the original Kim--Park, or to the proposed duality. With the recently developed deconfined perspective, this means all the working monopole deformed Kim--Park dualities up to quadratic terms are assembled by the Aharony and Benini-Benvenuti-Pasquetti dualities.