Anomaly inflow for subsystem symmetries

We study 't Hooft anomalies and the related anomaly inflow for subsystem global symmetries. These symmetries arise in a number of exotic systems, including models with fracton order such as X-cube model. As is case ordinary symmetries, can be canceled by from bulk theory one higher dimension; corresponding therefore non-trivial symmetry protected topological (SSPT) phase. demonstrate these phenomena several examples continuous discrete well time-reversal symmetry. For each example we describe boundary anomaly, present classical continuum actions SSPT phases, which response background gauge fields associated Interestingly, show that does not uniquely specify In general, latter may also depend on how foliation structure are extended into bulk.