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Discrete theta angles, symmetries and anomalies

Hsin, Po-Shen and Lam, Ho Tat (2021) Discrete theta angles, symmetries and anomalies. SciPost Physics, 10 (2). Art. No. 32. ISSN 2542-4653. doi:10.21468/scipostphys.10.2.032.

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Gauge theories in various dimensions often admit discrete theta angles, that arise from gauging a global symmetry with an additional symmetry protected topological (SPT) phase. We discuss how the global symmetry and 't Hooft anomaly depends on the discrete theta angles by coupling the gauge theory to a topological quantum field theory (TQFT). We observe that gauging an Abelian subgroup symmetry, that participates in symmetry extension, with an additional SPT phase leads to a new theory with an emergent Abelian symmetry that also participates in a symmetry extension. The symmetry extension of the gauge theory is controlled by the discrete theta angle which comes from the SPT phase. We find that discrete theta angles can lead to two-group symmetry in 4d QCD with SU(N), SU(N)/Z_k or SO(N) gauge groups as well as various 3d and 2d gauge theories.

Item Type:Article
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URLURL TypeDescription Paper
Hsin, Po-Shen0000-0002-4764-1476
Additional Information:© 2021 P.-S. Hsin and H. T. Lam. This work is licensed under the Creative Commons Attribution 4.0 International License. Published by the SciPost Foundation. Received 20-09-2020; Accepted 04-02-2021; Published 12-02-2021. We thank Yasunori Lee, Kantaro Ohmori, Nathan Seiberg, Shu-Heng Shao, Yuji Tachikawa and Juven Wang for discussions. We thank Nathan Seiberg, Shu-Heng Shao and Yuji Tachikawa for comments on a draft. The work of P.-S. H. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632, and by the Simons Foundation through the Simons Investigator Award. H.T.L. is supported by a Croucher Scholarship for Doctoral Study, a Centennial Fellowship from Princeton University and Physics Department of Princeton University.
Group:Walter Burke Institute for Theoretical Physics
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Department of Energy (DOE)DE-SC0011632
Simons FoundationUNSPECIFIED
Croucher FoundationUNSPECIFIED
Princeton UniversityUNSPECIFIED
Issue or Number:2
Record Number:CaltechAUTHORS:20210322-101122932
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:108504
Deposited By: Tony Diaz
Deposited On:23 Mar 2021 15:54
Last Modified:16 Nov 2021 19:12

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