Topological Spherical T-duality -- Dimension change from higher degree $H$-flux
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| author | Cavalcanti, Gil R. Heemskerk, Bart Uribe, Bernardo |
| author_facet | Cavalcanti, Gil R. Heemskerk, Bart Uribe, Bernardo |
| contents | Topological Spherical T-duality was introduced by Bouwknegt, Evslin and Mathai in [BEM15] as an extension of topological T-duality from $S^1$-bundles to $\mathrm{SU}(2)$-bundles endowed with closed 7-forms. This notion was further extended to sphere bundles by Lind, Sati and Westerland [LSW16] as a duality between $S^{2n-1}$-bundles endowed with closed $(4n-1)$-forms. We generalise this relation one step further and define T-duality for $S^{2n-1}$-bundles endowed with closed odd forms of arbitrary degree. The degree of the form determines the dimension of the fibers of the dual spaces. We show that $T$-duals exist and, as in the previous cases, $T$-dual spaces have isomorphic twisted cohomology. We finish by introducing a version of Courant algebroids which is compatible with spherical T-duality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_14054 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Topological Spherical T-duality -- Dimension change from higher degree $H$-flux Cavalcanti, Gil R. Heemskerk, Bart Uribe, Bernardo Differential Geometry High Energy Physics - Theory 55R25, 57R22, 57R19, 57N65 Topological Spherical T-duality was introduced by Bouwknegt, Evslin and Mathai in [BEM15] as an extension of topological T-duality from $S^1$-bundles to $\mathrm{SU}(2)$-bundles endowed with closed 7-forms. This notion was further extended to sphere bundles by Lind, Sati and Westerland [LSW16] as a duality between $S^{2n-1}$-bundles endowed with closed $(4n-1)$-forms. We generalise this relation one step further and define T-duality for $S^{2n-1}$-bundles endowed with closed odd forms of arbitrary degree. The degree of the form determines the dimension of the fibers of the dual spaces. We show that $T$-duals exist and, as in the previous cases, $T$-dual spaces have isomorphic twisted cohomology. We finish by introducing a version of Courant algebroids which is compatible with spherical T-duality. |
| title | Topological Spherical T-duality -- Dimension change from higher degree $H$-flux |
| topic | Differential Geometry High Energy Physics - Theory 55R25, 57R22, 57R19, 57N65 |
| url | https://arxiv.org/abs/2405.14054 |