Feynman Graph Integrals on Kähler Manifolds
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911267344613376 |
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| author | Wang, Minghao Yan, Junrong |
| author_facet | Wang, Minghao Yan, Junrong |
| contents | In this paper, we establish the convergence of Feynman graph integrals on closed real-analytic Kähler manifolds and uncover the structural mechanism underlying this convergence. The key insight is that, using Getzler's rescaling technique, the graph integrands extend canonically to the Fulton-MacPherson compactification of configuration spaces as forms with divisorial-type singularities. This allows the Feynman graph integrals to be rigorously defined as Cauchy principal value integrals. As an application, these integrals provide a mathematically rigorous construction of the higher-genus B-model invariants on Calabi-Yau threefolds in the sense of Bershadsky-Cecotti-Ooguri-Vafa (BCOV). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09170 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Feynman Graph Integrals on Kähler Manifolds Wang, Minghao Yan, Junrong Mathematical Physics Differential Geometry 81Q30, 81T15, 81T20, 81T70, 14N35: 53D45 In this paper, we establish the convergence of Feynman graph integrals on closed real-analytic Kähler manifolds and uncover the structural mechanism underlying this convergence. The key insight is that, using Getzler's rescaling technique, the graph integrands extend canonically to the Fulton-MacPherson compactification of configuration spaces as forms with divisorial-type singularities. This allows the Feynman graph integrals to be rigorously defined as Cauchy principal value integrals. As an application, these integrals provide a mathematically rigorous construction of the higher-genus B-model invariants on Calabi-Yau threefolds in the sense of Bershadsky-Cecotti-Ooguri-Vafa (BCOV). |
| title | Feynman Graph Integrals on Kähler Manifolds |
| topic | Mathematical Physics Differential Geometry 81Q30, 81T15, 81T20, 81T70, 14N35: 53D45 |
| url | https://arxiv.org/abs/2507.09170 |