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

TL;DR

This paper investigates the low energy dynamics of SU(2) Yang-Mills theory with a theta term at , focusing on how anomalies and symmetry enrichments influence possible phases, domain walls, and quantum critical points.

Contribution

It introduces the concept of Gauge Enhanced Quantum Critical Points and analyzes the role of topological terms and anomalies in SU(2) Yang-Mills theory.

Findings

Identification of  domain wall symmetry and enrichment effects.

Relation between SU(2) Yang-Mills and U(1) Maxwell gauge theories in symmetry context.

Proposal of phase transitions involving gauge group enhancement at criticality.

Abstract

We explore the low energy dynamics of the four siblings of Lorentz symmetry enriched SU(2) Yang-Mills theory with a theta term at $\theta=\pi$ in $(3+1)$d. Due to 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 is described by a U(1) Maxwell gauge theory (e.g. U(1) spin liquid in condensed matter) 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 $\mathbb{Z}_2$ unitary symmetry on the domain wall. We discuss how the Lorentz symmetry and the unitary $\mathbb{Z}_2$ symmetry enrich 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) 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.