Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory

TL;DR

This work demonstrates that, in the planar ('t Hooft) limit, higher-loop contributions can be expressed entirely in terms of one-loop amplitudes and conjecture an analogous relation for n-point amplitudes.

Abstract

The collinear factorization properties of two-loop scattering amplitudes in dimensionally-regulated N=4 super-Yang-Mills theory suggest that, in the planar ('t Hooft) limit, higher-loop contributions can be expressed entirely in terms of one-loop amplitudes. We demonstrate this relation explicitly for the two-loop four-point amplitude and, based on the collinear limits, conjecture an analogous relation for n-point amplitudes. The simplicity of the relation is consistent with intuition based on the AdS/CFT correspondence that the form of the large N_c L-loop amplitudes should be simple enough to allow a resummation to all orders.

Figures (2)

• Figure 1: The collinear factorization of a two-loop amplitude. In each term in the sum, the left blob is a splitting amplitude, and the right blob an $(n-1)$-point scattering amplitude.
• Figure 2: The scalar integral functions appearing in the (a) one- and (b) two-loop four-point $N=4$ amplitudes.