Anomaly constraint on chiral central charge of (2+1)d topological order
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 w...
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| Format: | Article |
| Language: | English |
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American Physical Society
2021-05-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.3.023107 |
| _version_ | 1797211091514687488 |
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| author | Ryohei Kobayashi |
| author_facet | Ryohei Kobayashi |
| author_sort | Ryohei Kobayashi |
| collection | DOAJ |
| description | 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 ν∈Z_{16}, the TQFT must have c_{−}=1/4 mod 1/2 for odd ν, while c_{−}=0 mod 1/2 for even ν. 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. |
| first_indexed | 2024-04-24T10:20:59Z |
| format | Article |
| id | doaj.art-e27e34a254bf49e9986b0286bbf745d9 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:20:59Z |
| publishDate | 2021-05-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-e27e34a254bf49e9986b0286bbf745d92024-04-12T17:09:47ZengAmerican Physical SocietyPhysical Review Research2643-15642021-05-013202310710.1103/PhysRevResearch.3.023107Anomaly constraint on chiral central charge of (2+1)d topological orderRyohei KobayashiIn 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 ν∈Z_{16}, the TQFT must have c_{−}=1/4 mod 1/2 for odd ν, while c_{−}=0 mod 1/2 for even ν. 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.http://doi.org/10.1103/PhysRevResearch.3.023107 |
| spellingShingle | Ryohei Kobayashi Anomaly constraint on chiral central charge of (2+1)d topological order Physical Review Research |
| title | Anomaly constraint on chiral central charge of (2+1)d topological order |
| title_full | Anomaly constraint on chiral central charge of (2+1)d topological order |
| title_fullStr | Anomaly constraint on chiral central charge of (2+1)d topological order |
| title_full_unstemmed | Anomaly constraint on chiral central charge of (2+1)d topological order |
| title_short | Anomaly constraint on chiral central charge of (2+1)d topological order |
| title_sort | anomaly constraint on chiral central charge of 2 1 d topological order |
| url | http://doi.org/10.1103/PhysRevResearch.3.023107 |
| work_keys_str_mv | AT ryoheikobayashi anomalyconstraintonchiralcentralchargeof21dtopologicalorder |