Skip to main content

Research Repository

Advanced Search

Leading singularities and off-shell conformal integrals

Drummond, James; Duhr, Claude; Eden, Burkhard; Heslop, Paul; Pennington, Jeffrey; Smirnov, Vladimir A.

Leading singularities and off-shell conformal integrals Thumbnail


James Drummond

Claude Duhr

Burkhard Eden

Jeffrey Pennington

Vladimir A. Smirnov


The three-loop four-point function of stress-tensor multiplets in N = 4 super Yang-Mills theory contains two so far unknown, off-shell, conformal integrals, in addition to the known, ladder-type integrals. In this paper we evaluate the unknown integrals, thus obtaining the three-loop correlation function analytically. The integrals have the generic structure of rational functions multiplied by (multiple) polylogarithms. We use the idea of leading singularities to obtain the rational coefficients, the symbol — with an appropriate ansatz for its structure — as a means of characterising multiple polylogarithms, and the technique of asymptotic expansion of Feynman integrals to obtain the integrals in certain limits. The limiting behaviour uniquely fixes the symbols of the integrals, which we then lift to find the corresponding polylogarithmic functions. The final formulae are numerically confirmed. The techniques we develop can be applied more generally, and we illustrate this by analytically evaluating one of the integrals contributing to the same four-point function at four loops. This example shows a connection between the leading singularities and the entries of the symbol.


Drummond, J., Duhr, C., Eden, B., Heslop, P., Pennington, J., & Smirnov, V. A. (2013). Leading singularities and off-shell conformal integrals. Journal of High Energy Physics, 2013(8), Article 133.

Journal Article Type Article
Publication Date Aug 29, 2013
Deposit Date Nov 21, 2013
Publicly Available Date Jan 14, 2014
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Electronic ISSN 1029-8479
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2013
Issue 8
Article Number 133
Keywords Supersymmetric gauge theory, Scattering amplitudes, Extended supersymmetry.


Published Journal Article (827 Kb)

Publisher Licence URL

Copyright Statement
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.

You might also like

Downloadable Citations