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. We illustrate this proposal through the examples of the abelian Higgs model in 2d, as well as adjoint QCD and N = 4 super Yang-Mills in 4d. We also comment on how the ’t Hooft anomalies of non-invertible symmetries impose new constraints on the dynamics.
Bibliographical notePublisher Copyright:
© 2023, The Author(s).
- Anomalies in Field and String Theories
- Global Symmetries
- Topological States of Matter
ASJC Scopus subject areas
- Nuclear and High Energy Physics