@article{TEXTUAL,
      recid = {12177},
      author = {Córdova, Clay and Ohmori, Kantaro and Shao, Shu-Heng and  Yan, Fei},
      title = {Decorated $Z_2$ symmetry defects and their time-reversal  anomalies},
      journal = {Physical Review D},
      address = {2020-08-27},
      number = {TEXTUAL},
      abstract = {We discuss an isomorphism between the possible anomalies  of $(d+1)$-dimensional quantum field theories with $Z_2$  unitary global symmetry, and those of d-dimensional quantum  field theories with time-reversal symmetry $T$. This  correspondence is an instance of symmetry defect  decoration. The worldvolume of a $Z_2$ symmetry defect is  naturally invariant under $T$, and bulk $Z_2$ anomalies  descend to $T$ anomalies on these defects. We illustrate  this correspondence in detail for $(1+1)d$ bosonic systems  where the bulk $Z_2$ anomaly leads to a Kramers degeneracy  in the symmetry defect Hilbert space and exhibits examples.  We also discuss $(1+1)d$ fermion systems protected by $Z_2$  global symmetry where interactions lead to a $Z_8$  classification of anomalies. Under the correspondence, this  is directly related to the $Z_8$ classification of $(0+1)d$  fermions protected by T. Finally, we consider $(3+1)d$  bosonic systems with $Z_2$ symmetry where the possible  anomalies are classified by $Z_2×Z_2$. 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.$},
      url = {http://knowledge.uchicago.edu/record/12177},
}