  We study 't Hooft anomalies for discrete global symmetries in bosonic
theories in 2, 3 and 4 dimensions. We show that such anomalies may arise in
gauge theories with topological terms in the action, if the total symmetry
group is a nontrivial extension of the global symmetry by the gauge symmetry.
Sometimes the 't Hooft anomaly for a d-dimensional theory with a global
symmetry G can be canceled by anomaly inflow from a (d+1)-dimensional
topological gauge theory with gauge group G. Such d-dimensional theories can
live on the surfaces of Symmetry Protected Topological Phases. We also give
examples of theories with more severe 't Hooft anomalies which cannot be
canceled in this way.

High Energy Physics - Theory;Strongly Correlated Electrons