Analytic result for a two-loop five-particle amplitude

TL;DR

This work provides the first analytic symbol for a full-color two-loop five-point amplitude in N=4 super Yang-Mills, including non-planar subleading-color terms. It constructs a uniform transcendental weight master integral basis, derives canonical differential equations with a 31-letter pentagon alphabet, and expresses the amplitude as Parke-Taylor prefactors multiplying UT integrals, with stringent checks on collinear limits and infrared factorization. The authors also analyze the multi-Regge limit, finding a vanishing symbol-level contribution from the double-trace sector and deriving leading subleading-power logarithmic corrections, thereby revealing a compact structure guided by the non-planar alphabet. These results furnish a rich analytic data set for testing infrared factorization, Regge behavior, and potential hidden symmetries, and pave the way for higher-loop explorations in non-planar sectors.

Abstract

We compute the symbol of the full-color two-loop five-particle amplitude in $\mathcal{N}=4$ super Yang-Mills, including all non-planar subleading-color terms. The amplitude is written in terms of permutations of Parke-Taylor tree-level amplitudes and pure functions to all orders in the dimensional regularization parameter, in agreement with previous conjectures. The answer has the correct collinear limits and infrared factorization properties, allowing us to define a finite remainder function. We study the multi-Regge limit of the non-planar terms, analyze its subleading power corrections, and present analytically the leading logarithmic terms.

Figures (1)

• Figure 1: Diagrams in the representation of Carrasco:2011mn of the integrand of the two-loop five-point amplitude in $\mathcal{N}=4$ sYM. We omit the associated numerators and color factors.