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| Главные авторы: | , , , |
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| Формат: | Preprint |
| Опубликовано: |
2023
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| Предметы: | |
| Online-ссылка: | https://arxiv.org/abs/2312.02148 |
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Оглавление:
- We study the twisted (co)homology of a family of genus-one integrals -- the so called Riemann-Wirtinger integrals. These integrals are closely related to one-loop string amplitudes in chiral splitting where one leaves the loop-momentum, modulus and all but one puncture un-integrated. While not actual one-loop string integrals, they share many properties and are simple enough that the associated twisted (co)homologies have been completely characterized [Goto2022,arXiv:2206.03177]. Using intersection numbers -- an inner product on the vector space of allowed differential forms -- we derive the Gauss-Manin connection for two bases of the twisted cohomology providing an independent check of [Mano&Watanabe2012]. We also use the intersection index -- an inner product on the vector space of allowed contours -- to derive a double-copy formula for the closed-string analogues of Riemann-Wirtinger integrals (one-dimensional integrals over the torus). Similar to the celebrated KLT formula between open- and closed-string tree-level amplitudes, these intersection indices form a genus-one KLT-like kernel defining bilinears in meromorphic Riemann-Wirtinger integrals that are equal to their complex counterparts.