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

Physical Review Letters
Jacob L BourjailyMatthias Wilhelm

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

References

Jan 24, 2015·Physical Review Letters·Nima Arkani-HamedJaroslav Trnka
Nov 26, 2016·Physical Review Letters·Ömer Gürdoğan, Vladimir Kazakov
Dec 24, 2016·Physical Review Letters·Simon Caron-HuotMatt von Hippel
Mar 31, 2018·Physical Review Letters·David GrabnerGregory Korchemsky
Apr 26, 2018·Physical Review Letters·Jacob L BourjailyMatthias Wilhelm

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Citations

Feb 9, 2019·Physical Review Letters·Jacob L BourjailyMatthias Wilhelm
Jun 11, 2021·Physical Review Letters·Jacob L BourjailyMarcus Spradlin

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