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 S U ( N ) / ℤ N gauge theory coupled to N_f N f flavors of Majorana fermions in the adjoint representation. For N N even and sufficiently large odd N_f N f , upon imposing time-reversal symmetry and an SO(N_f) S O ( N f ) flavor symmetry, the massless theory realizes a quantum critical point between a gapped phase in which a Z_N ℤ N one-form symmetry is completely broken and a phase where it is broken to Z_2 ℤ 2 , leading to ZN/2 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) S O ( N f ) flavor symmetry, for N N and N_f 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.