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

TL;DR

The work addresses the classification of 3d $\mathcal{N}=2$ Seiberg-like dualities for unitary gauge theories with adjoint matter under monopole deformations, focusing on terms up to quadratic order. It introduces a new linear-monopole-deformed duality KP$_{\alpha}^{\pm}$ and its two-monopole extension KP$_{\alpha,\beta}$, extends the dressing range to $\alpha\in[0,2p]$, and demonstrates consistency via superconformal index matches and F-maximization checks. A deconfined picture, built from Aharony and BBP dualities, is used to argue that all such monopole-deformed KP dualities arise from these building blocks, suggesting a unifying structure for KP-type dualities. The authors further classify generic monopole deformations, showing that, up to quadratic order, no new inequivalent dualities emerge beyond the KP family, reinforcing the view that Aharony and BBP underpin the entire landscape of these 3d Seiberg-like dualities. These results illuminate the organizing principle behind monopole dynamics in 3d adjoint SQCD and provide a robust framework for exploring IR dualities in similar settings.

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.