A 2d (0,2) appetizer

TL;DR

This work identifies the simplest non-abelian 2d $N=(0,2)$ gauge theory with nontrivial IR dynamics as SU(2) SQCD with $N_f=4$ chiral flavors, and posits a dual $(0,2)$ Landau-Ginzburg model with a cubic superpotential $J = \Psi\ Pf(Phi)$. By linking to a 4d Seiberg-dual pair via compactification on $S^2$ with a partial twist, the authors map the 4d dual to the proposed 2d LG model and establish a coherent IR picture. The chiral algebra on both sides is shown to be the same, namely $so(8)_{-2}$, validating the duality at the level of BPS sectors and offering a nontrivial bridge to the 4d $\,\mathcal{N}=2$ result for SU(2) with four hypers. The classical moduli space appears as a complex cone over $Gr(2,4)$, with a Pfaffian Calabi-Yau realization and a deformation controlling the singularity; the quantum fate of this singularity and the normalizability of the vacuum remain open questions for further study.

Abstract

Searching for the simplest non-abelian 2d gauge theory with $\mathcal{N}=(0,2)$ supersymmetry and non-trivial IR physics, we propose a new duality for $SU(2)$ SQCD with $N_f = 4$ chiral flavors. The chiral algebra of this theory is found to be $\mathfrak{so}(8)_{-2}$, the same as in 4d $\mathcal{N}=2$ $SU(2)$ gauge theory with four hypermultiplets.