Constraints on Regge behaviour from IR physics

TL;DR

This paper derives positivity bounds on gravitational EFTs using crossing symmetric dispersion relations, linking IR physics to Regge behaviour and constraining the high-energy amplitude structure.

Contribution

It introduces a novel approach applying crossing symmetric dispersion relations to gravitational scattering, deriving sum rules that connect IR data to Regge trajectories.

Findings

Finite energy sum rule for gravity established

Regge trajectory constrained by positivity bounds

Unique determination of Regge trajectory in certain cases

Abstract

We consider positivity constraints applicable to the Effective Field Theory (EFT) of gravity in arbitrary dimensions. By considering scattering of indefinite initial and final states, we highlight the existence of a gravitational scattering amplitude for which full crossing symmetry is manifest and utilize the recently developed crossing symmetric dispersion relations to derive compact non-linear bounds. We show that the null constraints built into these dispersion relations lead to a finite energy sum rule for gravity which may be extended to a one-parameter family of continuous moment sum rules. These sum rules enforce a UV-IR relation which imposes constraints on both the Regge trajectory and residue. We also highlight a situation where the Regge trajectory is uniquely determined in terms of the sub-Regge scale amplitude. Generically the Regge behaviour may be split into an IR sensitive part calculable within a given EFT which mainly depends on the lightest fields in Nature, and an IR independent part which are subject to universal positivity constraints following from unitarity and analyticity.