Symmetry Enhancement, SPT Absorption, and Duality in QED$_3$

TL;DR

This paper explores the rich phase structure of QED$_3$ with two Dirac fermions, revealing how combining $O(4)$ theories explains SPT phases and anomalies, and predicts behaviors like monopole condensation in strongly coupled regimes.

Contribution

It introduces the concept of 'SPT absorption' to unify phase diagrams of $O(4)$ theories with QED$_3$, providing new insights into strongly coupled limits and topological phenomena.

Findings

Reproduction of SPT phases and anomalies through $O(4)$ theories

Prediction of monopole condensation leading to $ heta=rac{ ext{pi}}$ sigma models

Concrete phase diagram insights for strongly coupled QED$_3$

Abstract

Quantum Electrodynamics in 2+1 dimensions (QED$_3$) with two Dirac fermions displays time reversal symmetry, nontrivial SPT phases and anomalies. The fate of this theory in its strongly coupled regime has been debated extensively. Surprisingly, we find that gluing together the phase diagrams of two standard Wilson-Fisher $O(4)$ theories suffices to reproduce all the SPT phases, anomalies, and semi-classical limits. A central mechanism behind it is ``SPT absorption''. The patching of the $O(4)$ transitions makes very concrete predictions for the behavior of the theory in its strongly coupled limits; for instance, the $\theta=\pi$ sigma model with $S^3$ topology appears due to monopole condensation.