Finite energy sum rules for gravitational Regge amplitudes

TL;DR

This paper introduces a framework using finite energy sum rules to derive consistency constraints on gravitational Regge amplitudes, linking ultraviolet and infrared physics without super-Planckian issues.

Contribution

It develops a novel method to connect gravitational Regge amplitudes at finite energies with low-energy physics, deriving bounds without assuming permutation symmetry.

Findings

Derived multiple FESRs independent of permutation invariance

Established bounds on Regge parameters using crossing symmetry and unitarity

Produced infrared finite gravitational positivity bounds in four dimensions

Abstract

We develop a framework to derive consistency constraints on gravitational Regge amplitudes based on the finite energy sum rules (FESRs), which directly connect gravitational Regge amplitudes at a finite ultraviolet scale with infrared physics without suffering from super-Planckian physics. For illustration, we consider four-point scattering of an identical massless scalar coupled to gravity. First, we derive multiple FESRs without relying on the $s\text{-}t\text{-}u$ permutation invariance. We then make use of FESRs, crossing symmetry, and other principles such as unitarity, to derive bounds on the Regge parameters. The bounds result in infrared finite gravitational positivity bounds in four spacetime dimensions.