A proof of the weak gravity conjecture

Abstract

The weak gravity conjecture suggests that, in a self-consistent theory of quantum gravity, the strength of gravity is bounded from above by the strengths of the various gauge forces in the theory. In particular, this intriguing conjecture asserts that in a theory describing a U(1) gauge field coupled consistently to gravity, there must exist a particle whose proper mass is bounded (in Planck units) by its charge: $m/m_{\text{P}}<q$. This beautiful and remarkably compact conjecture has attracted the attention of physicists and mathematicians over the last decade. It should be emphasized, however, that despite the fact that there are numerous examples from field theory and string theory that support the conjecture, we still lack a general proof of its validity. In the present Letter we prove that the weak gravity conjecture (and, in particular, the mass-charge upper bound $m/m_{\text{P}}<q$) can be inferred directly from Bekenstein's generalized second law of thermodynamics, a law which is widely believed to reflect a fundamental aspect of the elusive theory of quantum gravity.

7 pages. This essay is awarded 4th Prize in the 2017 Essay Competition of the Gravity Research Foundation

References in corpus (6)

• Super-Planckian Spatial Field Variations and Quantum Gravity
• Universal Bound on Dynamical Relaxation Times and Black-Hole Quasinormal Ringing
• Dark energy from the string axiverse
• Infrared Consistency and the Weak Gravity Conjecture
• Quasinormal modes of charged fields around a Reissner-Nordström black hole
• The bound on viscosity and the generalized second law of thermodynamics

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