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Traintracks through Calabi-Yau Manifolds: Scattering Amplitudes beyond Elliptic Polylogarithms

Bourjaily, J. L., He, Y. ORCID: 0000-0002-0787-8380, McLeod, A. J. , von Hippel, M. & Wilhelm, M. (2018). Traintracks through Calabi-Yau Manifolds: Scattering Amplitudes beyond Elliptic Polylogarithms. Physical Review Letter, 121(7), article number 071603. doi: 10.1103/physrevlett.121.071603


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 manifolds. 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 φ4 theory to integrable theories including maximally supersymmetric Yang-Mills theory in the planar limit—a fact we demonstrate.

Publication Type: Article
Additional Information: Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Subjects: Q Science > QC Physics
Departments: School of Science & Technology > Mathematics
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