Gravity loop integrands from the ultraviolet

TL;DR

This paper reveals surprising ultraviolet properties of gravity loop integrands, showing improved scaling at high energies and proposing a new geometric perspective for graviton amplitudes, with implications for recursion relations.

Contribution

It uncovers enhanced UV behavior of gravity integrands and introduces a homogeneous construction method fixing integrands from vanishing conditions, suggesting a new geometric framework.

Findings

Improved UV scaling of multi-particle cuts up to seven loops.

Homogeneous integrand construction from vanishing conditions.

Connection between behavior at infinity and tree-level amplitude scaling.

Abstract

We demonstrate that loop integrands of (super-)gravity scattering amplitudes possess surprising properties in the ultraviolet (UV) region. In particular, we study the scaling of multi-particle unitarity cuts for asymptotically large momenta and expose an improved UV behavior of four-dimensional cuts through seven loops as compared to standard expectations. For N=8 supergravity, we show that the improved large momentum scaling combined with the behavior of the integrand under BCFW deformations of external kinematics uniquely fixes the loop integrands in a number of non-trivial cases. In the integrand construction, all scaling conditions are homogeneous. Therefore, the only required information about the amplitude is its vanishing at particular points in momentum space. This homogeneous construction gives indirect evidence for a new geometric picture for graviton amplitudes similar to the one found for planar N=4 super Yang-Mills theory. We also show how the behavior at infinity is related to the scaling of tree-level amplitudes under certain multi-line chiral shifts which can be used to construct new recursion relations.