Supersymmetric Topological Sigma Models and Doubling Spaces
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916847418343424 |
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| author | Halmrast, Daniel M. |
| author_facet | Halmrast, Daniel M. |
| contents | Witten's topological B-model on a Calabi-Yau background is known to reproduce, in the open string sector, the derived category of coherent sheaves. When the target space is a complex torus, the topological model enjoys a non-geometric symmetry known as T-duality, which relates the theories on the torus and dual torus backgrounds. By considering the "double field theory" of Hull and Reid-Edwards on the product of a torus and its dual, T-duality occurs as a geometric symmetry of the target space.
Building on the methods of Y. Qin, we propose a method of analyzing the topological B-model on a torus in the doubled geometry framework which naturally incorporates certain rank-one D-branes, providing a different perspective on the derived category of the torus. In certain cases, the intersection theory of these lifted branes correctly computes the BRST cohomology of the B-model, and hence the derived Hom-spaces of the corresponding line bundles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_08181 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Supersymmetric Topological Sigma Models and Doubling Spaces Halmrast, Daniel M. Differential Geometry Algebraic Geometry Witten's topological B-model on a Calabi-Yau background is known to reproduce, in the open string sector, the derived category of coherent sheaves. When the target space is a complex torus, the topological model enjoys a non-geometric symmetry known as T-duality, which relates the theories on the torus and dual torus backgrounds. By considering the "double field theory" of Hull and Reid-Edwards on the product of a torus and its dual, T-duality occurs as a geometric symmetry of the target space. Building on the methods of Y. Qin, we propose a method of analyzing the topological B-model on a torus in the doubled geometry framework which naturally incorporates certain rank-one D-branes, providing a different perspective on the derived category of the torus. In certain cases, the intersection theory of these lifted branes correctly computes the BRST cohomology of the B-model, and hence the derived Hom-spaces of the corresponding line bundles. |
| title | Supersymmetric Topological Sigma Models and Doubling Spaces |
| topic | Differential Geometry Algebraic Geometry |
| url | https://arxiv.org/abs/2507.08181 |