Generalized symmetry enriched criticality in (3+1)d

We construct two classes of continuous phase transitions in 3+1 dimensions between phases that break distinct generalized global symmetries. Our analysis focuses on SU (N) /ZN gauge theory coupled to Nf flavors of Majorana fermions in the adjoint representation. For N even and sufficiently large odd Nf, upon imposing time-reversal symmetry and an SO (Nf) flavor symmetry, the massless theory realizes a quantum critical point between two gapped phases: one in which a ZN one-form symmetry is completely broken and another where it is broken to Z₂, leading to Z₍/₂ topological order. We provide an explicit lattice model that exhibits this 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 (Nf) flavor symmetry, for N and Nf 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.