Decorated symmetry defects and their time-reversal anomalies
We discuss an isomorphism between the possible anomalies of ($$\textit{d}$$ + 1)-dimensional quantum field theories with $$\mathbb{Z}_2$$ unitary global symmetry, and those of $$\textit{d}$$-dimensional quantum field theories with time-reversal symmetry T. This correspondence is an instance of symmetry defect decoration. The worldvolume of a $$\mathbb{Z}_2$$ symmetry defect is naturally invariant under T, and bulk $$\mathbb{Z}_2$$ anomalies descend to T anomalies on these defects. We illustrate this correspondence in detail for (1 + 1)$$\textit{d}$$ bosonic systems where the bulk $$\mathbb{Z}_2$$ anomaly leads to a Kramers degeneracy in the symmetry defect Hilbert space and exhibits examples. We also discuss (1 + 1)$$\textit{d}$$ fermion systems protected by $$\mathbb{Z}_2$$ global symmetry where interactions lead to a $$\mathbb{Z}_8$$ classification of anomalies. Under the correspondence, this is directly related to the $$\mathbb{Z}_8$$ classification of (0 + 1)$$\textit{d}$$ fermions protected by T. Finally, we consider (3 + 1)$$\textit{d}$$ bosonic systems with $$\mathbb{Z}_2$$ symmetry where the possible anomalies are classified by $$\mathbb{Z}_2$$ × $$\mathbb{Z}_2$$. We construct topological field theories realizing these anomalies and show that their associated symmetry defects support anyons that can be either fermions or Kramers doublets.
- Research Organization:
- Rutgers Univ., Piscataway, NJ (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC); National Science Foundation (NSF); Simons Foundation
- Grant/Contract Number:
- SC0010008; PHY-1606531
- OSTI ID:
- 1651180
- Alternate ID(s):
- OSTI ID: 1802025
- Journal Information:
- Physical Review D, Journal Name: Physical Review D Vol. 102 Journal Issue: 4; ISSN 2470-0010
- Publisher:
- American Physical SocietyCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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