Generalized symmetry enriched criticality in (3+1)d

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)/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 Z_N one-form symmetry is completely broken and a phase where it is broken to Z₂, leading to Z_N/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(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.