Symmetry TFTs and anomalies of non-invertible symmetries

Justin Kaidi, Emily Nardoni, Gabi Zafrir, Yunqin Zheng

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number53
JournalJournal of High Energy Physics
Issue number10
StatePublished - Oct 2023
Externally publishedYes

Bibliographical note

Publisher 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


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