Modular constraints on conformal field theories with currents
We study constraints coming from the modular invariance of the partition function of two-dimensional conformal field theories. We constrain the spectrum of CFTs in the presence of holomorphic and anti-holomorphic currents using the semi-definite programming. In particular, we find the bounds on the...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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Springer
2017
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| _version_ | 1826296819981746176 |
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| author | Bae, J-B Lee, S Song, J |
| author_facet | Bae, J-B Lee, S Song, J |
| author_sort | Bae, J-B |
| collection | OXFORD |
| description | We study constraints coming from the modular invariance of the partition function of two-dimensional conformal field theories. We constrain the spectrum of CFTs in the presence of holomorphic and anti-holomorphic currents using the semi-definite programming. In particular, we find the bounds on the twist gap for the non-current primaries depend dramatically on the presence of holomorphic currents, showing numerous kinks and peaks. Various rational CFTs are realized at the numerical boundary of the twist gap, saturating the upper limits on the degeneracies. Such theories include Wess-Zumino-Witten models for the Deligne’s exceptional series, the Monster CFT and the Baby Monster CFT. We also study modular constraints imposed by W-algebras of various type and observe that the bounds on the gap depend on the choice of W-algebra in the small central charge region.
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| first_indexed | 2024-03-07T04:22:13Z |
| format | Journal article |
| id | oxford-uuid:cb664450-0269-401a-823f-94bfba8853a6 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T04:22:13Z |
| publishDate | 2017 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:cb664450-0269-401a-823f-94bfba8853a62022-03-27T07:14:37ZModular constraints on conformal field theories with currentsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:cb664450-0269-401a-823f-94bfba8853a6EnglishSymplectic ElementsSpringer2017Bae, J-BLee, SSong, JWe study constraints coming from the modular invariance of the partition function of two-dimensional conformal field theories. We constrain the spectrum of CFTs in the presence of holomorphic and anti-holomorphic currents using the semi-definite programming. In particular, we find the bounds on the twist gap for the non-current primaries depend dramatically on the presence of holomorphic currents, showing numerous kinks and peaks. Various rational CFTs are realized at the numerical boundary of the twist gap, saturating the upper limits on the degeneracies. Such theories include Wess-Zumino-Witten models for the Deligne’s exceptional series, the Monster CFT and the Baby Monster CFT. We also study modular constraints imposed by W-algebras of various type and observe that the bounds on the gap depend on the choice of W-algebra in the small central charge region. |
| spellingShingle | Bae, J-B Lee, S Song, J Modular constraints on conformal field theories with currents |
| title | Modular constraints on conformal field theories with currents |
| title_full | Modular constraints on conformal field theories with currents |
| title_fullStr | Modular constraints on conformal field theories with currents |
| title_full_unstemmed | Modular constraints on conformal field theories with currents |
| title_short | Modular constraints on conformal field theories with currents |
| title_sort | modular constraints on conformal field theories with currents |
| work_keys_str_mv | AT baejb modularconstraintsonconformalfieldtheorieswithcurrents AT lees modularconstraintsonconformalfieldtheorieswithcurrents AT songj modularconstraintsonconformalfieldtheorieswithcurrents |