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| Format: | Preprint |
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2025
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| Online-Zugang: | https://arxiv.org/abs/2504.20358 |
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| _version_ | 1866918151144341504 |
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| author | Han, Fei Mathai, Varghese |
| author_facet | Han, Fei Mathai, Varghese |
| contents | The main purpose of this paper is to establish the loop space formulation of T-duality in the presence of background flux. In particular, we construct a loop space analogue of the Hori formula, termed \textbf{the loop Hori map}, and demonstrate that it induces a quasi-isomorphism between the exotic twisted equivariant cohomologies on the free loop spaces of the T-dual sides. Spacetime, when viewed as the constant loops, is a submanifold of loop space. The duality that we prove on loop space restricts to the T-duality with $H$-flux on spacetime. This significantly refines the earlier work of the authors in 2015 where T-duality was established after localisation to the base space. The construction of the loop Hori map is an application of our generalization of the Bismut--Chern character in 2015, originally introduced in the loop space interpretation of the Atiyah--Singer index theorem by Atiyah--Witten and Bismut. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_20358 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Loop Hori Formulae for T-duality and Twisted Bismut-Chern Character Han, Fei Mathai, Varghese High Energy Physics - Theory Differential Geometry The main purpose of this paper is to establish the loop space formulation of T-duality in the presence of background flux. In particular, we construct a loop space analogue of the Hori formula, termed \textbf{the loop Hori map}, and demonstrate that it induces a quasi-isomorphism between the exotic twisted equivariant cohomologies on the free loop spaces of the T-dual sides. Spacetime, when viewed as the constant loops, is a submanifold of loop space. The duality that we prove on loop space restricts to the T-duality with $H$-flux on spacetime. This significantly refines the earlier work of the authors in 2015 where T-duality was established after localisation to the base space. The construction of the loop Hori map is an application of our generalization of the Bismut--Chern character in 2015, originally introduced in the loop space interpretation of the Atiyah--Singer index theorem by Atiyah--Witten and Bismut. |
| title | Loop Hori Formulae for T-duality and Twisted Bismut-Chern Character |
| topic | High Energy Physics - Theory Differential Geometry |
| url | https://arxiv.org/abs/2504.20358 |