Anomaly inflow for subsystem symmetries

Fiona J. Burnell, Trithep Devakul, Pranay Gorantla, Ho Tat Lam, Shu Heng Shao

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We study 't Hooft anomalies and the related anomaly inflow for subsystem global symmetries. These symmetries and anomalies arise in a number of exotic systems, including models with fracton order such as the X-cube model. As is the case for ordinary global symmetries, anomalies for subsystem symmetries can be canceled by anomaly inflow from a bulk theory in one higher dimension; the corresponding bulk is therefore a nontrivial subsystem symmetry protected topological (SSPT) phase. We demonstrate these phenomena in several examples with continuous and discrete subsystem global symmetries, as well as time-reversal symmetry. For each example we describe the boundary anomaly, and present classical continuum actions for the corresponding bulk SSPT phases, which describe the response of background gauge fields associated with the subsystem symmetries. Interestingly, we show that the anomaly does not uniquely specify the bulk SSPT phase. In general, the latter may also depend on how the symmetry and the associated foliation structure on the boundary are extended into the bulk.

Original languageEnglish (US)
Article number085113
JournalPhysical Review B
Issue number8
StatePublished - Aug 15 2022

Bibliographical note

Funding Information:
We thank N. Seiberg for suggesting this topic to us and for initial collaborations in this project. We also thank Z. Komargodski and K. Ohmori for discussions. F.J.B. is grateful for the financial support of the Carnegie corporation of New York, and of the National Science foundation NSF Grant No. DMR 1928166. P.G. was supported by the Physics Department of Princeton University. H.T.L. was supported in part by a Centennial Fellowship and a Charlotte Elizabeth Procter Fellowship from Princeton University, a Croucher fellowship from the Croucher Foundation, the Packard Foundation, the Physics Department of Princeton University and the Center for Theoretical Physics at MIT. S.-H.S. was supported by the Simons Collaboration on Ultra-Quantum Matter, which is a grant from the Simons Foundation (651440, NS). The authors of this paper were ordered alphabetically.

Publisher Copyright:
© 2022 American Physical Society.


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