Nonsupersymmetric dualities from mirror symmetry

TL;DR

This work addresses how non-supersymmetric 3d dualities can be derived from the basic $N=2$ chiral mirror symmetry between a free chiral multiplet and $N=2$ SQED with one flavor. By perturbing with SUSY-breaking operators and tracking their dual mappings, the authors obtain a four-phase diagram with dual critical theories along the phase boundaries, yielding explicit dual pairs that relate scalar QED to a free fermion and Wilson-Fisher fixed points to both scalar and fermionic QED. They further show how modular transformations $S$ and $T$ relate these dualities, positioning the supersymmetric mirror symmetry as a multicritical parent that organizes a web of non-SUSY 3d dualities. The results have potential applications to condensed-matter problems such as quantum Hall plateau transitions and metallic criticality, providing a unified framework that connects bosonic and fermionic QED and Wilson-Fisher physics through a single starting point. Overall, the paper strengthens the bridge between SUSY dualities and non-SUSY 3d dualities, offering a principled method to generate and relate dual descriptions across bosonic and fermionic sectors.

Abstract

We study supersymmetry breaking perturbations of the simplest dual pair of 2+1-dimensional N = 2 supersymmetric field theories -- the free chiral multiplet and N = 2 super-QED with a single flavor. We find dual descriptions of a phase diagram containing four distinct massive phases. The equivalence of the intervening critical theories gives rise to several non-supersymmetric avatars of mirror symmetry: we find dualities relating scalar QED to a free fermion and Wilson-Fisher theories to both scalar and fermionic QED. Thus, mirror symmetry can be viewed as the multicritical parent duality from which these non-supersymmetric dualities directly descend.

Figures (2)

• Figure 1: Phase diagram of theory A. Massless fields occur along the red lines (second order phase transitions).
• Figure 2: Phase diagram of theory B.