IR Dualities in General 3d Supersymmetric SU(N) QCD Theories

TL;DR

The paper addresses IR dualities for 3d ${\cal N}=2$ SU(N) CS QCD with general numbers of fundamental and antifundamental flavors and nonzero CS level. By starting from the known SU(N) dual for $F=\tilde{F}$ and flowing via real mass deformations, the authors derive the IR duals for generic $(N,F,\tilde{F},k)$, distinguishing two regimes based on $\Delta F=|F-\tilde{F}|$ relative to $2k$. The duals take the form $SU(N)_{\tilde{k}} \leftrightarrow SU(F_{\max}-N)_{-\tilde{k}} \times U(1)_{F_{\max}-N-\tilde{k}}$ with mesons coupled by $W=M q \tilde{q}$ in the $\Delta F \le 2k$ case, and a second regime with an extra $U(1)_0$ factor for $\Delta F > 2k$, plus a matching structure in the dual with appropriate rank shifts. A nontrivial consistency check is provided by matching baryonic flat directions across the duality, supporting the validity of these new SU(N) dual pairs and linking them to the broader landscape of 3d dualities with $U(N)$ roots.

Abstract

In the last twenty years, low-energy (IR) dualities have been found for many pairs of supersymmetric gauge theories with four supercharges, both in four space-time dimensions and in three space-time dimensions. In particular, duals have been found for 3d N=2 supersymmetric QCD theories with gauge group U(N), with F chiral multiplets in the fundamental representation, with F' chiral multiplets in the anti-fundamental representation, and with Chern-Simons level k, for all values of N, F, F' and k for which the theory preserves supersymmetry. For SU(N) theories the duals have been found in some cases, such as F=F' and F'=0, but not in the general case. In this note we find the IR dual for SU(N) SQCD theories with general values of N, F, F' and a non-zero k, which preserve supersymmetry.