@article{30485c8920ea4a1bb63061133e30569e,
title = "Traintracks through Calabi-Yau Manifolds: Scattering Amplitudes beyond Elliptic Polylogarithms",
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 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.",
author = "Bourjaily, {Jacob L.} and He, {Yang Hui} and McLeod, {Andrew J.} and {Von Hippel}, Matt and Matthias Wilhelm",
note = "Funding Information: This work was supported in part by the Danish Independent Research Fund under Grant No.DFF-4002-00037 (M.W.); Danish National Research Foundation under Grant No.DNRF91, a grant from the Villum Fonden and a Starting Grant (No.757978) from the European Research Council (J.L.B., A.J.M., M.v.H., M.W). Y.H.H. would like to thank the Science and Technology Facilities Council, UK, for Grant No.ST/J00037X/1, the Chinese Ministry of Education, for a Chang-Jiang Chair Professorship at NanKai University as well as the City of Tian-Jin for a Qian-Ren Scholarship, and Merton College, Oxford, for her enduring support. Publisher Copyright: {\textcopyright} 2018 authors. Published by the American Physical Society.",
year = "2018",
month = aug,
day = "17",
doi = "10.1103/PhysRevLett.121.071603",
language = "English (US)",
volume = "121",
journal = "Physical Review Letters",
issn = "0031-9007",
publisher = "American Physical Society",
number = "7",
}