Abstract
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 \( \mathcal{N} \) = 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.
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Acknowledgments
We thank Yichul Choi, Linhao Li, Kantaro Ohmori, Sakura Schafer-Nameki, Yuji Tachikawa, and Zheyan Wan for discussions. We thank Shu-Heng Shao and Yuji Tachikawa for comments on a draft. JK and GZ thank Kavli IPMU for their generous hospitality during the inception of this work. EN and YZ are partially supported by WPI Initiative, MEXT, Japan at IPMU, the University of Tokyo. GZ is partially supported by the Simons Foundation grant 815892.
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Kaidi, J., Nardoni, E., Zafrir, G. et al. Symmetry TFTs and anomalies of non-invertible symmetries. J. High Energ. Phys. 2023, 53 (2023). https://doi.org/10.1007/JHEP10(2023)053
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DOI: https://doi.org/10.1007/JHEP10(2023)053