Journal of High Energy Physics

, 2016:115 | Cite as

Evaluating four-loop conformal Feynman integrals by D-dimensional differential equations

  • Burkhard EdenEmail author
  • Vladimir A. Smirnov
Open Access
Regular Article - Theoretical Physics


We evaluate a four-loop conformal integral, i.e. an integral over four four-dimensional coordinates, by turning to its dimensionally regularized version and applying differential equations for the set of the corresponding 213 master integrals. To solve these linear differential equations we follow the strategy suggested by Henn and switch to a uniformly transcendental basis of master integrals. We find a solution to these equations up to weight eight in terms of multiple polylogarithms. Further, we present an analytical result for the given four-loop conformal integral considered in four-dimensional space-time in terms of single-valued harmonic polylogarithms. As a by-product, we obtain analytical results for all the other 212 master integrals within dimensional regularization, i.e. considered in D dimensions.


Conformal Field Theory Scattering Amplitudes Supersymmetric gauge theory 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Supplementary material

13130_2016_4886_MOESM1_ESM.m (83 kb)
ESM 1 (M 83 kb)
13130_2016_4886_MOESM2_ESM.m (13 kb)
ESM 2 (M 13 kb)


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Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.Institut für Mathematik und PhysikHumboldt-Universität zu BerlinBerlinGermany
  2. 2.Skobeltsyn Institute of Nuclear PhysicsMoscow State UniversityMoscowRussia

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