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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/2312.11268 |
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| _version_ | 1866916599165878272 |
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| author | Davidović, Ljubica Ivanišević, Ilija Sazdović, Branislav |
| author_facet | Davidović, Ljubica Ivanišević, Ilija Sazdović, Branislav |
| contents | This paper investigates the simultaneous twisting of the Courant bracket by a 2-form $B$ and a bi-vector $θ$, exploring the generalized fluxes obtained in Courant algebroid relations. We define the twisted Lie bracket and demonstrate that the generalized $H$-flux can be expressed as the field strength defined on this Lie algebroid. Similarly, we show that the $f$-flux is a direct consequence of simultaneous twisting, which arises in the twisted Lie bracket relations between holonomic partial derivatives. We obtain the generalized $Q$ flux in terms of the twisted Koszul bracket, which is a quasi-Lie algebroid bracket. The action of an exterior derivative related to the twisted Koszul bracket on a bi-vector produces the generalized $R$-flux. We show that the generalized $R$-flux is also the twisted Schouten-Nijenhuis bracket, i.e. the natural graded bracket on multi-vectors defined with the twisted Lie bracket. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_11268 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fluxes of Courant bracket twisted at the same time by $B$ and $θ$ Davidović, Ljubica Ivanišević, Ilija Sazdović, Branislav High Energy Physics - Theory This paper investigates the simultaneous twisting of the Courant bracket by a 2-form $B$ and a bi-vector $θ$, exploring the generalized fluxes obtained in Courant algebroid relations. We define the twisted Lie bracket and demonstrate that the generalized $H$-flux can be expressed as the field strength defined on this Lie algebroid. Similarly, we show that the $f$-flux is a direct consequence of simultaneous twisting, which arises in the twisted Lie bracket relations between holonomic partial derivatives. We obtain the generalized $Q$ flux in terms of the twisted Koszul bracket, which is a quasi-Lie algebroid bracket. The action of an exterior derivative related to the twisted Koszul bracket on a bi-vector produces the generalized $R$-flux. We show that the generalized $R$-flux is also the twisted Schouten-Nijenhuis bracket, i.e. the natural graded bracket on multi-vectors defined with the twisted Lie bracket. |
| title | Fluxes of Courant bracket twisted at the same time by $B$ and $θ$ |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2312.11268 |