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

A bstract We propose a new 3d $$ \mathcal{N}=2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:math> 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.