We explore the low-energy dynamics of the four siblings of Lorentz symmetry enriched $\mathrm{SU}\left(2\right)$ Yang-Mills theories with a theta term at $\theta =\pi$ in $(3+1)\mathrm{d}$. Due to a mixed anomaly between time reversal symmetry and the one-form center symmetry, the low-energy dynamics cannot be symmetric trivially gapped. We focus on two possible scenarios: (1) time reversal symmetry is spontaneously broken by the two confining vacua and (2) a deconfined, gapless, and time reversal symmetric $\mathrm{U}\left(1\right)$ Maxwell gauge theory [e.g., $\mathrm{U}\left(1\right)$ spin liquid in condensed matter]. In the first scenario, we find that the antiunitary time reversal symmetry in the bulk induces a ${\mathbb{Z}}_2$ unitary symmetry on the domain wall between the two vacua. We discuss how the Lorentz symmetry and the unitary ${\mathbb{Z}}_2$ symmetry enrich the domain-wall topological field theory. In the second scenario, we relate the symmetry enrichments of the $\mathrm{SU}\left(2\right)$ Yang-Mills to that of the $\mathrm{U}\left(1\right)$ Maxwell gauge theory. This further opens up the possibility that $\mathrm{SU}\left(2\right)$ QCD with large and odd flavors of fermions could be a direct second-order phase transition between two phases of $\mathrm{U}\left(1\right)$ gauge theories as well as between a $\mathrm{U}\left(1\right)$ gauge theory and a trivial vacuum (e.g., a trivial paramagnet), where the gauge group is enhanced to be non-Abelian at and only at the transition. We characterize these transitions and name them as gauge enhanced quantum critical points.

• Received 16 November 2019
• Accepted 6 January 2020

DOI:https://doi.org/10.1103/PhysRevResearch.2.013189

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society