Traintracks through Calabi-Yau Manifolds: Scattering Amplitudes beyond Elliptic Polylogarithms.
Phys Rev Lett
; 121(7): 071603, 2018 Aug 17.
Article
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| MEDLINE
| ID: mdl-30169053
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.
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Phys Rev Lett
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2018
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Article
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Dinamarca