Unravelling the Holomorphic Twist: Central Charges
The holomorphic twist provides a powerful framework to study minimally protected sectors in supersymmetric quantum field theories. We investigate the algebraic structure underlying the holomorphic twist of N=1 superconformal field theories in four dimensions. In particular, in holomorphically twiste...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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Springer
2024
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| _version_ | 1826315247459237888 |
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| author | Bomans, P Wu, J |
| author_facet | Bomans, P Wu, J |
| author_sort | Bomans, P |
| collection | OXFORD |
| description | The holomorphic twist provides a powerful framework to study minimally protected sectors in supersymmetric quantum field theories. We investigate the algebraic structure underlying the holomorphic twist of N=1 superconformal field theories in four dimensions. In particular, in holomorphically twisted theories the flavour and conformal symmetry algebras are enhanced to infinite-dimensional higher Kac Moody and higher Virasoro symmetry algebras respectively. We explicitly compute the binary and ternary λ-brackets and clarify their relation with the underlying infinite-dimensional symmetry algebra. Doing so we show that the central extensions of said symmetry algebras precisely encode the conformal anomalies a and c as well as the flavour central charges of the physical four-dimensional theory. This parallels the familiar story in two dimensions where the conformal anomaly c is encoded in the central extension of the Virasoro algebra. |
| first_indexed | 2024-12-09T03:22:23Z |
| format | Journal article |
| id | oxford-uuid:7f6dba6e-227d-40ab-9a7f-29748af00ae1 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-12-09T03:22:23Z |
| publishDate | 2024 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:7f6dba6e-227d-40ab-9a7f-29748af00ae12024-11-16T20:04:51ZUnravelling the Holomorphic Twist: Central ChargesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:7f6dba6e-227d-40ab-9a7f-29748af00ae1EnglishJisc Publications RouterSpringer2024Bomans, PWu, JThe holomorphic twist provides a powerful framework to study minimally protected sectors in supersymmetric quantum field theories. We investigate the algebraic structure underlying the holomorphic twist of N=1 superconformal field theories in four dimensions. In particular, in holomorphically twisted theories the flavour and conformal symmetry algebras are enhanced to infinite-dimensional higher Kac Moody and higher Virasoro symmetry algebras respectively. We explicitly compute the binary and ternary λ-brackets and clarify their relation with the underlying infinite-dimensional symmetry algebra. Doing so we show that the central extensions of said symmetry algebras precisely encode the conformal anomalies a and c as well as the flavour central charges of the physical four-dimensional theory. This parallels the familiar story in two dimensions where the conformal anomaly c is encoded in the central extension of the Virasoro algebra. |
| spellingShingle | Bomans, P Wu, J Unravelling the Holomorphic Twist: Central Charges |
| title | Unravelling the Holomorphic Twist: Central Charges |
| title_full | Unravelling the Holomorphic Twist: Central Charges |
| title_fullStr | Unravelling the Holomorphic Twist: Central Charges |
| title_full_unstemmed | Unravelling the Holomorphic Twist: Central Charges |
| title_short | Unravelling the Holomorphic Twist: Central Charges |
| title_sort | unravelling the holomorphic twist central charges |
| work_keys_str_mv | AT bomansp unravellingtheholomorphictwistcentralcharges AT wuj unravellingtheholomorphictwistcentralcharges |