Dualities for three-dimensional $\mathcal{N} = 2$ $SU(N_c)$ chiral adjoint SQCD

TL;DR

This paper classifies dualities in 3d $ abla$ $ ext{SU}(N_c)$ SQCD with an adjoint and polynomial superpotential, using flow analysis and partition function matching, and compares with non-adjoint cases.

Contribution

It provides a complete classification of chiral dualities in 3d $ ext{SU}(N_c)$ SQCD with an adjoint, based on differences in fundamentals and antifundamentals and Chern-Simons level.

Findings

Classification of dualities based on $|N_f - N_a|$ and $k$.

Matching of three-sphere partition functions supports the dualities.

Comparison with non-adjoint SQCD cases confirms consistency.

Abstract

We study dualities for 3d $\mathcal{N} = 2$ $SU(N_c)$ SQCD at Chern-Simons level $k$ in presence of an adjoint with polynomial superpotential. The dualities are dubbed chiral because there is a different amount of fundamentals $N_f$ and antifundamentals $N_a$. We build a complete classification of such dualities in terms of $ |N_f - N_a| $ and $k$. The classification is obtained by studying the flow from the non-chiral case, and we corroborate our proposals by matching the three-sphere partition functions. Finally, we revisit the case of $SU(N_c)$ SQCD without the adjoint, comparing our results with previous literature.