2021/01/31 by Ryohei Kobayashi · 5 citations
Physics and Astronomy · #Anomaly (physics) #Black Holes and Theoretical Physics #Central charge #Charge (physics) #Chiral anomaly #Physics of Superconductivity and Magnetism #Quantum field theory #Topological Materials and Phenomena #Topological order #Topological quantum field theory #Topological quantum number #Topology (electrical circuits) #cond-mat.str-el #hep-th
paper · pdf · doi:10.1103/physrevresearch.3.023107
published in Physical Review Research 3(2) (American Physical Society) · 16 pages, 2 figures, references added, accepted in Physical Review Research
openalex created_date 2021/03/29 · arxiv created 2021/05/07 · openalex publication_date 2021/05/10 · arxiv updated 2021/05/19 · openalex updated_date 2026/08/05
In this short paper, we argue that the chiral central charge c -of a (2 + 1)d topological ordered state is sometimes strongly constrained by 't Hooft anomaly of antiunitary global symmetry. For example, if a (2 + 1)d fermionic topological quantum field theory (TQFT) has a time-reversal anomaly with T 2 = (-1) F labeled as Z 16 , the TQFT must have c -= 1/4 mod 1/2 for odd , while c -= 0 mod 1/2 for even . This generalizes the fact that the bosonic TQFT with T anomaly in a particular class must carry c -= 4 mod 8 to fermionic cases. We also study such a constraint for fermionic TQFT with U (1) CT symmetry, which is regarded as a gapped surface of the topological superconductor in class AIII.