Discrete theta angles, symmetries and anomalies

Journal Article · Fri Feb 12 00:00:00 EST 2021 · SciPost Physics

DOI:https://doi.org/10.21468/SciPostPhys.10.2.032· OSTI ID:1765416

Hsin, Po-Shen ^[1]; Lam, Ho Tat ^[2]

---

1. Walter Burke Institute for Theoretical Physics
2. Princeton University

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 $4d$ QCD with SU(N),SU(N)/\mathbb{Z}_k $SU\left(N\right),SU\left(N\right)/{\mathbb{Z}}_k$ or SO(N) $SO\left(N\right)$ gauge groups as well as various 3d $3d$ and 2d $2d$ gauge theories.

• Sponsoring Organization: USDOE
• Grant/Contract Number: SC0011632
• OSTI ID: 1765416
• Journal Information: SciPost Physics, Journal Name: SciPost Physics Vol. 10 Journal Issue: 2; ISSN 2542-4653
• Publisher: Stichting SciPost
• Country of Publication: Netherlands
• Language: English