Scalar weak gravity bound from full unitarity

TL;DR

This paper derives a new bound on the ratio of the EFT cutoff to the Planck mass using unitarity and causality constraints, addressing challenges posed by graviton poles in scattering amplitudes.

Contribution

It introduces a novel method to bound the EFT cutoff scale relative to the Planck mass by analyzing IR divergences and unitarity, applicable to theories with gravity.

Findings

EFT cutoff scale must be below approximately 10 times the Planck mass.

New dispersion relation approach handles graviton pole divergences.

Full unitarity of partial wave expansion incorporated in the analysis.

Abstract

Weak gravity conjecture can be formulated as a statement that gravity must be the weakest force, compared to the other interactions in low energy effective field theory (EFT). Several arguments in favor of this statement were presented from the side of string theory and black hole physics. However, it is still an open question whether the statement of weak gravity can be proven based on more general assumptions of causality, unitarity, and locality of the fundamental theory. These consistency requirements imply the dispersion relations for the scattering amplitudes which allow to bound the EFT coefficients. The main difficulty for obtaining these constraints in the presence of gravity is related to the graviton pole which makes the required dispersion relations divergent in the forward limit. In this work, we present a new way of deriving the bound on the ratio between the EFT cutoff scale and Planck mass from confronting the IR divergences from graviton pole and one-loop running of the EFT Wilson coefficient in front of the dimension-12 operator. Our method also allows the incorporation of full unitarity of partial wave expansion of the UV theory. We examine the EFT of a single shift-symmetric scalar in four dimensions and find that the maximal value of the cutoff scale of the EFT coupled to gravity must be lower than about $O(10)$ Planck mass.