One-loop SYM-supergravity relation for five-point amplitudes

TL;DR

The paper establishes a precise one-loop connection between N=8 supergravity and the subleading-color sector of N=4 SYM at five points by recasting the SYM amplitude in a color–trace basis via the color–kinematic dual CJ representation. It proves a linear relation ${\mathcal M}_5^{(1)} = -\frac{1}{20 i g^5} (\kappa/2)^5 \sum_{S_5} \tilde{\beta}_{12345} A_{5;3}(12;345)$, exploiting IR-divergence matching ($1/\epsilon$) and the independence of kinematic numerators from loop momentum. The result extends earlier four-point relations to five points and clarifies that the correspondence holds at the level of integrated amplitudes with a diagram-independent double-copy structure. The work highlights the role of subleading-color amplitudes in gravity/gauge links and suggests further exploration of relations beyond loop-momentum–independent numerators and across other multiplicities.

Abstract

We derive a linear relation between the one-loop five-point amplitude of N=8 supergravity and the one-loop five-point subleading-color amplitudes of N=4 supersymmetric Yang-Mills theory.

Figures (1)

• Figure 1: One-loop five-point diagrams