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Scalar weak gravity bound from full unitarity

Anna Tokareva1,2,5,* and Yongjun Xu1,3,4,†

  • *Contact author: tokareva@ucas.ac.cn
  • †Contact author: xuyongjun23@mails.ucas.ac.cn
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Phys. Rev. D 112, 085020 – Published 23 October, 2025

DOI: https://doi.org/10.1103/86hv-m36b

Abstract

The 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 us 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 the 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 the partial wave expansion of the UV theory. We examine the EFT of a single shift-symmetric scalar in four dimensions and find that the relation between the EFT coupling in front of the dimension-12 operator and the Planck mass.

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Phys. Rev. D 112, 085020– Published 23 October, 2025
  • Received 6 March 2025
  • Accepted 3 September 2025
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