  In many cases the symmetry structure of quantum field theories can be neatly
encoded into their associated symmetry theory (SymTFT), a topological field
theory in one dimension higher. For geometrically engineered QFTs in string
theory this SymTFT has been argued to arise from the background geometry,
essentially by integration of the topological sector of string theory on the
horizon of the geometry transverse to the QFT locus. In this paper we clarify
some subtle aspects of this proposal. We take a higher dimensional approach,
where the ten dimensional string theory fields to be integrated arise as edge
modes of a topological field theory in eleven dimensions. The resulting
construction provides a SymTFT generalisation of the descent procedure for
anomalies.
