Traintracks Through Calabi-Yaus: Amplitudes Beyond Elliptic Polylogarithms
| Autor: | Bourjaily, Jacob L., He, Yang-Hui, McLeod, Andrew J., von Hippel, Matt, Wilhelm, Matthias |
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| Rok vydání: | 2018 |
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| Zdroj: | Phys. Rev. Lett. 121, 071603 (2018) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevLett.121.071603 |
| Popis: | We describe a family of finite, four-dimensional, $L$-loop Feynman integrals that involve weight-$(L+1)$ hyperlogarithms integrated over $(L-1)$-dimensional elliptically fibered varieties we conjecture to be Calabi-Yau. At three loops, we identify the relevant K3 explicitly; and we provide strong evidence that the four-loop integral involves a Calabi-Yau threefold. These integrals are necessary for the representation of amplitudes in many theories---from massless $\varphi^4$ theory to integrable theories including maximally supersymmetric Yang-Mills theory in the planar limit---a fact we demonstrate. Comment: 4+2 pages, 4 figures; references added |
| Databáze: | arXiv |
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