T-Dualities and Courant Algebroid Relations
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arXiv
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| Format: | Preprint |
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2023
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| author | De Fraja, Thomas C. Marotta, Vincenzo Emilio Szabo, Richard J. |
| author_facet | De Fraja, Thomas C. Marotta, Vincenzo Emilio Szabo, Richard J. |
| contents | We develop a new approach to T-duality based on Courant algebroid relations which subsumes the usual T-duality as well as its various generalisations. Starting from a relational description for the reduction of exact Courant algebroids over foliated manifolds, we introduce a weakened notion of generalised isometries that captures the generalised geometry counterpart of Riemannian submersions when applied to transverse generalised metrics. This is used to construct T-dual backgrounds as generalised metrics on reduced Courant algebroids which are related by a generalised isometry. We prove an existence and uniqueness result for generalised isometric exact Courant algebroids coming from reductions. We demonstrate that our construction reproduces standard T-duality relations based on correspondence spaces. We also describe how it applies to generalised T-duality transformations of almost para-Hermitian manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_15147 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | T-Dualities and Courant Algebroid Relations De Fraja, Thomas C. Marotta, Vincenzo Emilio Szabo, Richard J. Differential Geometry High Energy Physics - Theory Mathematical Physics We develop a new approach to T-duality based on Courant algebroid relations which subsumes the usual T-duality as well as its various generalisations. Starting from a relational description for the reduction of exact Courant algebroids over foliated manifolds, we introduce a weakened notion of generalised isometries that captures the generalised geometry counterpart of Riemannian submersions when applied to transverse generalised metrics. This is used to construct T-dual backgrounds as generalised metrics on reduced Courant algebroids which are related by a generalised isometry. We prove an existence and uniqueness result for generalised isometric exact Courant algebroids coming from reductions. We demonstrate that our construction reproduces standard T-duality relations based on correspondence spaces. We also describe how it applies to generalised T-duality transformations of almost para-Hermitian manifolds. |
| title | T-Dualities and Courant Algebroid Relations |
| topic | Differential Geometry High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2308.15147 |