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

TL;DR

This paper explores dualities and symmetry enhancements in three-dimensional supersymmetric QED with 2 and 4 flavors, revealing stable fixed points with larger infrared symmetries through perturbative analysis.

Contribution

It demonstrates the emergence of enhanced symmetries in 3D sQED with 2 and 4 flavors and analyzes their stability using perturbative methods.

Findings

U(2) symmetry often enhances to O(4) or SU(3) in the IR

Superpotential deformations preserving U(2) are irrelevant at fixed points

An example with 4 flavors shows enhanced SO(6) symmetry

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.