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High Energy Physics - Theory

arXiv:1805.09326 (hep-th)
[Submitted on 23 May 2018 (v1), last revised 9 Aug 2018 (this version, v2)]

Title:Traintracks Through Calabi-Yaus: Amplitudes Beyond Elliptic Polylogarithms

Authors: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 $\varphi^4$ theory to integrable theories including maximally supersymmetric Yang-Mills theory in the planar limit---a fact we demonstrate.
Comments: 4+2 pages, 4 figures; references added
Subjects: High Energy Physics - Theory (hep-th); High Energy Physics - Phenomenology (hep-ph)
Cite as: arXiv:1805.09326 [hep-th]
  (or arXiv:1805.09326v2 [hep-th] for this version)
  https://doi.org/10.48550/arXiv.1805.09326
Journal reference: Phys. Rev. Lett. 121, 071603 (2018)
Related DOI: https://doi.org/10.1103/PhysRevLett.121.071603

Submission history

From: Jacob Bourjaily [view email]
[v1] Wed, 23 May 2018 18:00:00 UTC (68 KB)
[v2] Thu, 9 Aug 2018 16:10:40 UTC (68 KB)
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