Inherited Twistor-Space Structure of Gravity Loop Amplitudes

TL;DR

This work uses KLT relations and the unitarity method to relate one-loop ${\cal N}=8$ supergravity amplitudes to ${\cal N}=4$ super-Yang-Mills amplitudes, arguing that box integrals alone suffice and that their coefficients are given by products of YM box-coefficients. It demonstrates how NMHV and higher-point gravity box coefficients can be constructed from gauge-theory data, providing explicit six-, seven-, and eight-point examples. The authors also show that gravity amplitudes inherit the twistor-space structure of gauge theory, with gravity box coefficients exhibiting derivative-of-delta-function support on collinear or coplanar configurations corresponding to MHV, NMHV, and N$^2$MHV sectors. Together, these results suggest a powerful, gauge-theory-driven route to compute and understand loop-level gravity amplitudes and their geometric twistor properties, with potential implications for UV behavior and deeper string-theoretic connections.

Abstract

At tree-level, gravity amplitudes are obtainable directly from gauge theory amplitudes via the Kawai, Lewellen and Tye closed-open string relations. We explain how the unitarity method allows us to use these relations to obtain coefficients of box integrals appearing in one-loop N=8 supergravity amplitudes from the recent computation of the coefficients for N=4 super-Yang-Mills non-maximally-helicity-violating amplitudes. We argue from factorisation that these box coefficients determine the one-loop N=8 supergravity amplitudes, although this remains to be proven. We also show that twistor-space properties of the N=8 supergravity amplitudes are inherited from the corresponding properties of N=4 super-Yang-Mills theory. We give a number of examples illustrating these ideas.