Two-Loop Amplitudes of Gluons and Octa-Cuts in N=4 Super Yang-Mills

TL;DR

This paper introduces octa-cut techniques for calculating two-loop gluon amplitudes in N=4 super Yang-Mills, simplifying coefficient extraction by localizing integrals with additional propagator-like singularities.

Contribution

It presents a novel octa-cut method for two-loop amplitude calculations, extending the leading singularity analysis beyond traditional hepta-cuts.

Findings

Octa-cut localizes certain two-loop integrals with an additional propagator.

Coefficients of five- and six-gluon amplitudes are explicitly computed.

Method suggests potential for higher-loop generalizations.

Abstract

After reduction techniques, two-loop amplitudes in N=4 super Yang-Mills theory can be written in a basis of integrals containing scalar double-box integrals with rational coefficients, though the complete basis is unknown. Generically, at two loops, the leading singular behavior of a scalar double box integral with seven propagators is captured by a hepta-cut. However, it turns out that a certain class of such integrals has an additional propagator-like singularity. One can then formally cut the new propagator to obtain an octa-cut which localizes the cut integral just as a quadruple cut does at one-loop. This immediately gives the coefficient of the scalar double box integral as a product of six tree-level amplitudes. We compute, as examples, several coefficients of the five- and six-gluon non-MHV two-loop amplitudes. We also discuss possible generalizations to higher loops.