Symmetry TFTs and Anomalies of Non-Invertible Symmetries

Understand

It is known that the 't Hooft anomalies of invertible global symmetries can be characterized by an invertible TQFT in one higher dimension.

• The analogous statement remains to be understood for non-invertible symmetries.
• In this note we discuss how the linking invariants in a non-invertible TQFT known as the Symmetry TFT (SymTFT) can be used as a diagnostic for 't Hooft anomalies of non-invertible symmetries.
• When the non-invertible symmetry is non-intrinsically non-invertible, and hence the SymTFT is a Dijkgraaf-Witten model, the linking invariants can be computed explicitly.