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arXiv · 1805.09326

Traintracks Through Calabi-Yaus: Amplitudes Beyond Elliptic Polylogarithms

Jacob L. Bourjaily·Yang-Hui He·Andrew J. McLeod·Matt von Hippel·Matthias Wilhelm
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Abstract

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 $φ^4$ theory to integrable theories including maximally supersymmetric Yang-Mills theory in the planar limit---a fact we demonstrate.

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Jacob L. Bourjaily, Yang-Hui He, Andrew J. McLeod, Matt von Hippel, Matthias Wilhelm. 2018-08-09. Traintracks Through Calabi-Yaus: Amplitudes Beyond Elliptic Polylogarithms. https://doi.org/10.1103/physrevlett.121.071603

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