Bounding Violations of the Weak Gravity Conjecture

Abstract

The black hole weak gravity conjecture (WGC) is a set of linear inequalities on the four-derivative corrections to Einstein--Maxwell theory. Remarkably, in four dimensions, these combinations appear in the $2\to 2$ photon amplitudes, leading to the hope that the conjecture might be supported using dispersion relations. However, the presence of a pole arising in the forward limit due to graviton exchange greatly complicates the use of such arguments. In this paper, we apply recently developed numerical techniques to handle the graviton pole, and we find that standard dispersive arguments are not strong enough to imply the black hole WGC. Specifically, under a fairly typical set of assumptions, including weak coupling of the EFT and Regge boundedness, a small violation of the black hole WGC is consistent with unitarity and causality. We quantify the size of this violation, which vanishes in the limit where gravity decouples and also depends logarithmically on an infrared cutoff. We discuss the meaning of these bounds in various scenarios. We also implement a method for bounding amplitudes without manifestly positive spectral densities, which could be applied to any system of non-identical states, and we use it to improve bounds on the EFT of pure photons in absence of gravity.

55 pp

References in corpus (11)

• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Causality, Analyticity and an IR Obstruction to UV Completion
• Symmetries and Strings in Field Theory and Gravity
• Black Hole Bound on the Number of Species and Quantum Gravity at LHC
• Infrared Consistency and the Weak Gravity Conjecture
• Positivity of Curvature-Squared Corrections in Gravity
• Positivity Constraints for Pseudo-linear Massive Spin-2 and Vector Galileons
• Dispersion Relation Bounds for pi pi Scattering
• A note on Gauge Theories Coupled to Gravity
• The Other Fermion Compositeness
• Universal Bounds for SU(3) Low Energy Constants

Cited by in corpus (13)

• Graviton partial waves and causality in higher dimensions
• Classical vs Quantum Eikonal Scattering and its Causal Structure
• Moments for positivity: using Drell-Yan data to test positivity bounds and reverse-engineer new physics
• Nonperturbative Bounds on Scattering of Massive Scalar Particles in $d\ge 2$
• Bell inequalities in 2-2 scattering
• Bounds on photon scattering
• On (Scalar QED) Gravitational Positivity Bounds
• From Rotating to Charged Black Holes and Back Again
• Positivity bounds in vector theories
• Flat-space structure of gluon and graviton in AdS
• Locality and Analyticity of the Crossing Symmetric Dispersion Relation
• Quantum Corrections to Pair Production of Charged Black Holes in de Sitter Space
• Positivity bounds at one-loop level: the Higgs sector