Some aspects of symmetry descent

In many cases the symmetry structure of quantum field theories can be neatly encoded into their associated symmetry topological field 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.