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 (12)

• The String Landscape, Black Holes and Gravity as the Weakest Force
• Complexity Equals Action
• Entropy Bounds and Black Hole Remnants
• 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
• A massive charged scalar field in the Kerr-Newman background I: quasinormal modes, late-time tails and stability
• Warping the Weak Gravity Conjecture
• Modulated Natural Inflation
• 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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• Repulsive Forces and the Weak Gravity Conjecture
• A Holographic Derivation of the Weak Gravity Conjecture
• Swampland Variations on a Theme by KKLT
• Cosmic Censorship and Weak Gravity Conjecture in the Einstein-Maxwell-dilaton theory
• Flat Monodromies and a Moduli Space Size Conjecture
• Dimensional Reduction and (Anti) de Sitter Bounds
• The Weak Gravity Conjecture and the Axionic Black Hole Paradox
• Weak Gravity Conjecture from Conformal Field Theory: A Challenge from Hyperscaling Violating and Kerr-Newman-AdS Black Holes
• WGC and WCCC of black holes with quintessence and cloud strings in RPS space
• Quasinormal Modes of Charged Fields in Reissner-Nordstrom Backgrounds by Borel-Pade Summation of Bender-Wu Series
• WGC and WCC for charged black holes with quintessence and cloud of strings
• Scale and quality of Peccei-Quinn symmetry and weak gravity conjectures
• Fundamental Forces and Scalar Field Dynamics in the Early Universe
• Constraints on Early Dark Energy from the Axion Weak Gravity Conjecture
• Discrete Gauge Symmetries and the Weak Gravity Conjecture
• Extremal Bifurcations of Rotating AdS${}_4$ Black Holes
• Planar Black Holes as a Route to Understanding the Weak Gravity Conjecture
• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme
• The correlation of WGC and Hydrodynamics bound with $R^4$ correction in the charged AdS${}_{d+2}$ black brane
• De Sitter space constraints on brane tensions and couplings
• The quantum mass gap of extremal black holes