Generalized symmetry enriched criticality in (3+1)d

TL;DR

This paper constructs and analyzes novel continuous phase transitions in 3+1 dimensions involving generalized global symmetries, revealing critical points with enhanced and non-invertible symmetries, and providing explicit lattice models.

Contribution

It introduces new classes of critical points between gapped phases with different symmetry breaking patterns in 3+1D gauge theories, including models with non-invertible symmetries.

Findings

Critical points exhibit symmetry fractionalization patterns.

Explicit lattice models demonstrate the phase transitions.

Enhanced non-invertible symmetries appear at criticality.

Abstract

We construct two classes of continuous phase transitions in 3+1 dimensions between gapped phases that break distinct generalized global symmetries. Our analysis focuses on $SU(N)/\mathbb{Z}_N$ gauge theory coupled to $N_f$ flavors of Majorana fermions in the adjoint representation. For $N$ even and sufficiently large odd $N_f$, upon imposing time-reversal symmetry and an $SO(N_f)$ flavor symmetry, the massless theory realizes a quantum critical point between a gapped phase in which a $\mathbb{Z}_N$ one-form symmetry is completely broken and a phase where it is broken to $\mathbb{Z}_2$, leading to $\mathbb{Z}_{N/2}$ topological order. We characterize the possible patterns of symmetry fractionalization in these phases and provide an explicit lattice model that exhibits the transition. The critical point has an enhanced symmetry, which includes non-invertible analogues of time-reversal symmetry. Enforcing a non-invertible time-reversal symmetry and the $SO(N_f)$ flavor symmetry, for $N$ and $N_f$ both odd, we demonstrate that this critical point can appear between a topologically ordered phase and a phase that spontaneously breaks the non-invertible time-reversal symmetry, furnishing an analogue of deconfined quantum criticality for generalized symmetries.