Gauge Enhanced Quantum Criticality and Time Reversal Domain Wall: SU(2) Yang-Mills Dynamics with Topological Terms

We study the low energy dynamics of the four siblings of Lorentz symmetry enriched SU(2) Yang-Mills theory with a theta term at θ = π. Since there exists a mixed anomaly between time reversal symmetry and the center symmetry, the low energy dynamics must be nontrivial. We focus on two possible scenarios: 1) time reversal symmetry is spontaneously broken by the two confining vacua, and 2) the low energy theory describes a U(1) spin liquid which is deconfined and gapless while preserving time reversal symmetry. In the first scenario, we first identify the global symmetry on the time reversal domain wall, where time reversal symmetry in the bulk induces a Z2 unitary symmetry on the domain wall. We explore how the Lorentz symmetry and the unitary Z2 symmetry enriches the domain wall theory. In the second scenario, we relate the symmetry enrichments of the SU(2) Yang-Mills to that of the U(1) spin liquids. This further opens up the possibility that SU(2) QCD with large and odd flavors of fermions could be a second order phase transition between two phases of U(1) spin liquids as well as between a U(1) spin liquid and the a trivial paramagnet, where the gauge symmetry is enhanced to be non-Abelian at and only at the transition. We name them as Gauge Enhanced Quantum Critical Points.