N=1 QED in 2+1 dimensions: Dualities and enhanced symmetries

TL;DR

The paper studies 2+1D ${\mathcal{N}}=1$ (and related ${\mathcal{N}}=2,4$) sQEDs with two flavors and their dual Wess-Zumino models, uncovering infrared symmetry enhancements such as ${O(4)}$, ${SU(3)}$, and ${SO(6)}$. By mapping mesons and monopoles across dualities and performing a perturbative ${D=4-\varepsilon}$ analysis, it shows that ${SU(2)_{\text{flav}} \times U(1)_{\text{top}}}$-preserving deformations are irrelevant at the fixed points, implying stability of the enhanced-symmetry CFTs; it also constructs an ${\mathcal{N}}=2$ sQED with 4 flavors exhibiting ${SO(6)}$ enhancement. The work analyzes operator maps, deformations, and RG flows through dual WZ models, and provides nontrivial checks via the superconformal index and chiral ring structure, including an explicit ${SO(6)}$-covariant chiral ring relation and a complete-intersection moduli space. Together, these results support a coherent 3d duality web in which gauge theories, GN-Y models, and WZ theories realize IR symmetry enhancements that have parallels with non-supersymmetric QED dualities and may illuminate quantum phase transitions in 3d systems.

Abstract

We consider three-dimensional sQED with 2 flavors and minimal supersymmetry. We discuss various models which are dual to Gross-Neveu-Yukawa theories. The $U(2)$ ultraviolet global symmetry is often enhanced in the infrared, for instance to $O(4)$ or $SU(3)$. This is analogous to the conjectured behaviour of non-supersymmetric QED with 2 flavors. A perturbative analysis of the Gross-Neveu-Yukawa models in the $D = 4 - \varepsilon$ expansion shows that the $U(2)$ preserving superpotential deformations of the sQED (modulo tuning mass terms to zero) are irrelevant, so the fixed points with enhanced symmetry are stable. We also construct an example of $\mathcal{N} = 2$ sQED with 4 flavors that exhibits enhanced $SO(6)$ symmetry.