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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2311.04304 |
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| _version_ | 1866911791348449280 |
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| author | Bomans, Pieter Wu, Jingxiang |
| author_facet | Bomans, Pieter Wu, Jingxiang |
| contents | 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 $\mathcal{N} = 1$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_04304 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Unravelling the Holomorphic Twist: Central Charges Bomans, Pieter Wu, Jingxiang High Energy Physics - Theory Mathematical Physics 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 $\mathcal{N} = 1$ 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. |
| title | Unravelling the Holomorphic Twist: Central Charges |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2311.04304 |