2023/06/05 by Lei Su, Su, Lei
Physics and Astronomy · #Particle physics theoretical and experimental studies #Atomic and Subatomic Physics Research #Quantum Chromodynamics and Particle Interactions
paper · pdf · doi:10.48550/arxiv.2306.02976
Gauging a finite Abelian normal subgroup Γ of a nonanomalous 0-form symmetry G of a theory in (d+1)D spacetime can yield an unconventional critical point if the original theory has a continuous transition where Γ is completely spontaneously broken and if G is a nontrivial extension of G/Γ by Γ. The gauged theory has symmetry G/Γ× Γ(d-1), where Γ(d-1) is the (d-1)-form dual symmetry of Γ, and a 't Hooft anomaly between them. Thus it can be viewed as a boundary of a topological phase protected by G/Γ× Γ(d-1). The ordinary critical point, upon gauging, is mapped to a deconfined quantum critical point between two ordinary symmetry-breaking phases (d =1) or an unconventional quantum critical point between an ordinary symmetry-breaking phase and a topologically ordered phase (d≥ 2) associated with G/Γ and Γ(d-1), respectively. Order parameters and disorder parameters, before and after gauging, can be directly related. As a concrete example, we gauge the ℤ2 subgroup of ℤ4 symmetry of a 4-state clock model on a 1D lattice and a 2D square lattice. Since the symmetry of the clock model contains D8, the dihedral group of order 8, we also analyze the anomaly structure which is similar to that in the compactified SU(2) gauge theory with θ=π in (3+1)D and its mixed gauge theory. The general case is also discussed.