Gauge enhanced quantum criticality and time reversal deconfined domain wall: SU(2) Yang-Mills dynamics with topological terms

Abstract

We explore the low-energy dynamics of the four siblings of Lorentz symmetry enriched SU(2) Yang-Mills theories with a theta term at θ=π in (3+1)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 U(1) Maxwell gauge theory [e.g., U(1) spin liquid in condensed matter]. In the first scenario, we find that the antiunitary time reversal symmetry in the bulk induces a Z_{2} unitary symmetry on the domain wall between the two vacua. We discuss how the Lorentz symmetry and the unitary Z_{2} symmetry enrich the domain-wall topological field theory. In the second scenario, we relate the symmetry enrichments of the SU(2) Yang-Mills to that of the U(1) Maxwell gauge theory. This further opens up the possibility that SU(2) QCD with large and odd flavors of fermions could be a direct second-order phase transition between two phases of U(1) gauge theories as well as between a U(1) 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.