UV cancelations in gravity loop integrands

TL;DR

The paper investigates the ultraviolet structure of four-dimensional gravity loop integrands, focusing on how poles at infinity are absent for certain on-shell functions and how cancellations among different Feynman integrals arise in ${\mathcal N}=8$ supergravity (extending to pure gravity). By examining maximal and multi-unitarity cuts, the authors identify systematic cancellations that cannot be explained by known symmetries and argue that combining infrared constraints with these UV features could uniquely fix gravity amplitudes, potentially pointing to a geometric underpinning analogous to the Amplituhedron. They propose an all-loop cut conjecture and explore beyond-cut scenarios to demonstrate the persistence of these cancellations, suggesting a deep, yet-to-be-understood structure in gravity amplitudes. The findings hint at hidden properties of tree-level amplitudes and possible BCJ-related connections, with the long-term goal of achieving a non-perturbative, geometric formulation of gravity integrands that resolves labeling and non-planar issues.

Abstract

In this work we explore the properties of four-dimensional gravity integrands at large loop momenta. This analysis can not be done directly for the full off-shell integrand but only becomes well-defined on cuts that allow us to unambiguously specify labels for the loop variables. The ultraviolet region of scattering amplitudes originates from poles at infinity of the loop integrands and we show that in gravity these integcrands conceal a number of surprising features. In particular, certain poles at infinity are absent which requires a conspiracy between individual Feynman integrals contributing to the amplitude. We suspect that this non-trivial behavior is a consequence of yet-to-be found symmetry or hidden property of gravity amplitudes. We discuss mainly amplitudes in $\mathcal{N}=8$ supergravity but most of the statements are valid for pure gravity as well.