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

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.