Differential equations for multi-loop integrals and two-dimensional kinematics
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Publication:302993
DOI10.1007/JHEP04(2013)160zbMATH Open1342.81576arXiv1204.1031MaRDI QIDQ302993
Author name not available (Why is that?)
Publication date: 12 August 2016
Published in: (Search for Journal in Brave)
Abstract: In this paper we consider multi-loop integrals appearing in MHV scattering amplitudes of planar N=4 SYM. Through particular differential operators which reduce the loop order by one, we present explicit equations for the two-loop eight-point finite diagrams which relate them to massive hexagons. After the reduction to two-dimensional kinematics, we solve them using symbol technology. The terms invisible to the symbols are found through boundary conditions coming from double soft limits. These equations are valid at all-loop order for double pentaladders and allow to solve iteratively loop integrals given lower-loop information. Comments are made about multi-leg and multi-loop integrals which can appear in this special kinematics. The main motivation of this investigation is to get a deeper understanding of these tools in this configuration, as well as for their application in general four-dimensional kinematics and to less supersymmetric theories.
Full work available at URL: https://arxiv.org/abs/1204.1031
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