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On 2-group global symmetries and their anomalies

Journal of High Energy Physics volume 2019, Article number: 118 (2019) Cite this article

A preprint version of the article is available at arXiv.

Abstract

In general quantum field theories (QFTs), ordinary (0-form) global symmetries and 1-form symmetries can combine into 2-group global symmetries. We describe this phenomenon in detail using the language of symmetry defects. We exhibit a simple procedure to determine the (possible) 2-group global symmetry of a given QFT, and provide a classification of the related ’t Hooft anomalies (for symmetries not acting on spacetime). We also describe how QFTs can be coupled to extrinsic backgrounds for symmetry groups that differ from the intrinsic symmetry acting faithfully on the theory. Finally, we provide a variety of examples, ranging from TQFTs (gapped systems) to gapless QFTs. Along the way, we stress that the “obstruction to symmetry fractionalization” discussed in some condensed matter literature is really an instance of 2-group global symmetry.

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This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Authors and Affiliations

  1. SISSA, via Bonomea 265, Trieste, Italy

    Francesco Benini

  2. INFN — Sezione di Trieste, via Valerio 2, Trieste, Italy

    Francesco Benini

  3. School of Natural Sciences, Institute for Advanced Study, Princeton, NJ, U.S.A.

    Francesco Benini & Clay Córdova

  4. Physics Department, Princeton University, Princeton, NJ, U.S.A.

    Po-Shen Hsin

Authors
  1. Francesco Benini
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  2. Clay Córdova
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  3. Po-Shen Hsin
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Correspondence to Francesco Benini.

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ArXiv ePrint: 1803.09336

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Benini, F., Córdova, C. & Hsin, PS. On 2-group global symmetries and their anomalies. J. High Energ. Phys. 2019, 118 (2019). https://doi.org/10.1007/JHEP03(2019)118

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  • DOI: https://doi.org/10.1007/JHEP03(2019)118

Keywords

  • Global Symmetries
  • Anomalies in Field and String Theories
  • Chern-Simons Theories
  • Topological Field Theories