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In this work, we study unconventional anisotropic topologically orderedphases in 3d that manifest type-II fractonic physics along sub-manifolds. Whilethey behave as usual topological order along a preferred spatial direction,their physics along perpendicular planes is dictated by the presence of fractalsubsystem symmetries, completely restricting the mobility of anyonicexcitations and their bound states. We consider an explicit lattice modelrealization of such phases and proceed to study their properties under periodicboundary conditions and, later, in the presence of boundaries. We find that forspecific lattice sizes, the system possesses line and fractal membranesymmetries that are mutually anomalous, resulting in a non-trivially gappedground state space. This amounts to the spontaneous breaking of the fractalsymmetries, implying a sub-extensive ground state degeneracy. For the remainingsystem sizes the fractal symmetries are explicitly broken by the periodicboundary conditions, which is intrinsically related to the uniqueness of theground state. Despite of that, the system is still topologically ordered sincelocally created quasi-particles have nontrivial mutual statistics and, in thepresence of boundaries, it still presents anomalous edge modes. The intricatesymmetry interplay dictated by the lattice size is a wild manifestation ofultraviolet/infrared (UV/IR) mixing.

Fractal Subsystem Symmetries, 't Hooft Anomalies, and UV/IR Mixing