From the holomorphic Wilson loop to `d log' loop-integrands for super-Yang-Mills amplitudes.

Lipstein, Arthur E.; Mason, Lionel

Abstract

The S-matrix for planar = 4 super Yang-Mills theory can be computed as the correlation function for a holomorphic polygonal Wilson loop in twistor space. In an axial gauge, this leads to the construction of the all-loop integrand via MHV diagrams in twistor space. We show that at MHV, this formulation leads directly to expressions for loop integrands in d log form, i.e., the integrand is a product of exterior derivatives of logarithms of rational functions. For higher MHV degree, it is in d log form multiplied by delta functions. The parameters appearing in the d log form arise geometrically as the coordinates of insertion points of propagators on the holomorphic Wilson loop or on MHV vertices. We discuss a number of examples at one and two loops and give a preliminary discussion of the evaluation of the 1-loop MHV amplitude.

Citation

Lipstein, A. E., & Mason, L. (2013). From the holomorphic Wilson loop to `d log' loop-integrands for super-Yang-Mills amplitudes. Journal of High Energy Physics, 2013(05), Article 106. https://doi.org/10.1007/jhep05%282013%29106

• Journal Article Type: Article
• Acceptance Date: May 1, 2013
• Online Publication Date: May 21, 2013
• Publication Date: 2013-05
• Deposit Date: Feb 22, 2016
• Journal: Journal of High Energy Physics
• Print ISSN: 1126-6708
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2013
• Issue: 05
• Article Number: 106
• DOI: https://doi.org/10.1007/jhep05%282013%29106