Some aspects of symmetry descent

TL;DR

This paper explores the relationship between symmetry structures in quantum field theories and their topological field theory representations, clarifying subtle aspects using a higher-dimensional approach involving string theory and anomaly descent.

Contribution

It introduces a higher-dimensional framework where string theory fields act as edge modes of an eleven-dimensional topological field theory, extending the symmetry descent procedure.

Findings

Clarified the role of background geometry in SymTFT construction

Connected symmetry structures to topological field theories via higher dimensions

Extended anomaly descent to a topological field theory context

Abstract

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.