Symmetry TFTs from String Theory.

We determine the dimensional topological field theory, which encodes the higher-form symmetries and their 't Hooft anomalies for -dimensional QFTs obtained by compactifying M-theory on a non-compact space . The resulting theory, which we call the Symmetry TFT, or SymTFT for short, is derived by reducing the topological sector of 11d supergravity on the boundary of the space . Central to this endeavour is a reformulation of supergravity in terms of differential cohomology, which allows the inclusion of torsion in cohomology of the space , which in turn gives rise to the background fields for discrete (in particular higher-form) symmetries.