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Discrete Theta Angles, Symmetries and Anomalies

by Po-Shen Hsin, Ho Tat Lam

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Submission summary

As Contributors: Po-Shen Hsin · Ho Tat Lam
Preprint link: scipost_202102_00001v1
Date accepted: 2021-02-04
Date submitted: 2021-02-01 05:01
Submitted by: Lam, Ho Tat
Submitted to: SciPost Physics
Academic field: Physics
  • Condensed Matter Physics - Theory
  • High-Energy Physics - Theory
Approach: Theoretical


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 $SU(N),SU(N)/\mathbb{Z}_k$ or $SO(N)$ gauge groups as well as various 3d and 2d gauge theories.

Published as SciPost Phys. 10, 032 (2021)

Author comments upon resubmission

We thank the referees for comments and suggestions. We have added two footnotes and a paragraph to address the comments.

List of changes

1. Footnote 4 is added for a brief discussion on the $Sp(N)$ gauge theory.

2. Footnote 6 is added for a brief explanation of the Bockstein homomorphism, and for pointing the readers to relevant references.

3. First paragraph of section 2.1 is added for an explanation of symmetry fractionalization.

Reports on this Submission

Anonymous Report 1 on 2021-2-1 (Invited Report)


The authors have addressed the referee's comments satisfactorily. I recommend this article for publication in the SciPost.

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