Two-Loop Iteration of Five-Point N=4 Super-Yang-Mills Amplitudes

TL;DR

This confirmation of the iteration relation provides further evidence suggesting that N=4 gauge theory is solvable.

Abstract

We confirm by explicit computation the conjectured all-orders iteration of planar maximally supersymmetric N=4 Yang-Mills theory in the nontrivial case of five-point two-loop amplitudes. We compute the required unitarity cuts of the integrand and evaluate the resulting integrals numerically using a Mellin--Barnes representation and the automated package of ref.~[1]. This confirmation of the iteration relation provides further evidence suggesting that N=4 gauge theory is solvable.

Figures (3)

• Figure 1: The three- and two-particle cuts of the five-point amplitude.
• Figure 2: The two-loop integrals appearing in the five-point amplitude, with all external momenta flowing outwards. The normalization is as given in eq. (\ref{['Penta2MB']}), and the numerical labels on the internal propagators in (c) specify the arbitrary powers $a_i$. The prefactor in (c) is understood to be inserted in the numerator with power $-a_9$; in eq. (\ref{['TwoloopIntegrand']}), $-a_9 = 1$.
• Figure 3: The one-loop integrals required to all orders in $\epsilon$ for the one-loop five-point amplitude. The normalization is as given in eq. (\ref{['Penta1MB']}), and the numerical labels on the internal propagators in (b) specify the arbitrary powers $a_i$.