UV-Complete Gravity Amplitudes and the Triple Product

TL;DR

This paper constructs a new class of ultraviolet-complete four-graviton scattering amplitudes with a triple-product structure that match Einstein gravity at low energies and vanish at high energies, revealing an infinite spectrum of states.

Contribution

It introduces an infinite class of UV-complete gravity amplitudes with a novel triple-product form and an infinite tower of states, extending previous models of quantum gravity.

Findings

Amplitudes reduce to Einstein gravity at low energies.

Amplitudes vanish at high energies.

Spectrum contains infinite towers of states with positive residues.

Abstract

We construct an infinite class of new ultraviolet-complete four-graviton scattering amplitudes that reduce to Einstein gravity at low energies, vanish at high energies, are meromorphic, and exhibit a triple-product structure ${\cal A}(s){\cal A}(t){\cal A}(u)$. The spectrum invariantly exhibits accumulation points in the form of infinite towers of states on each mass pole, whose residue can be positively expanded on tree-level exchanges of irreducible representations of the Lorentz group.