A Holographic Derivation of the Weak Gravity Conjecture

Abstract

The Weak Gravity Conjecture (WGC) demands the existence of superextremal particles in any consistent quantum theory of gravity. The standard lore is that these particles are introduced to ensure that extremal black holes are either unstable or marginally stable, but it is not clear what is wrong if this doesn't happen. This note shows that, for a generic Einstein quantum theory of gravity in AdS, exactly stability of extremal black branes is in tension with rigorously proven quantum information theorems about entanglement entropy. Avoiding the contradiction leads to a nonperturbative version of the WGC, which reduces to the usual statement at weak coupling. The argument is general, and it does not rely on either supersymmetry or a particular UV completion, assuming only the validity of Einsteinian gravity, effective field theory, and holography. The pathology is related to the development of an infinite throat in the near-horizon region of the extremal solutions, which suggests a connection to the ER=EPR proposal.

36 pages + appendices; 6 figures. v2: Minor changes, expanded discussion in appendix B

References in corpus (48)

• On the Geometry of the String Landscape and the Swampland
• Symmetries and Strings in Field Theory and Gravity
• Distance and de Sitter Conjectures on the Swampland
• Holography from Conformal Field Theory
• Area laws in quantum systems: mutual information and correlations
• The String Landscape and the Swampland
• Aspects of generic entanglement
• $\mathcal{N}=1$ supersymmetric indices and the four-dimensional A-model
• Tensionless Strings and the Weak Gravity Conjecture
• Super-Planckian Spatial Field Variations and Quantum Gravity
• The landscape, the swampland and the era of precision cosmology
• Constraints on symmetry from holography
• A Stringy Test of the Scalar Weak Gravity Conjecture
• Weak Gravity Conjecture from Unitarity and Causality
• The Weak Gravity Conjecture in three dimensions
• Infinite Distance Networks in Field Space and Charge Orbits
• Natural Inflation and Quantum Gravity
• De Sitter vs Quintessence in String Theory
• Dark Energy in the Swampland
• The dS swampland conjecture and the Higgs potential
• On the Possibility of Large Axion Moduli Spaces
• Entropy Function and AdS(2)/CFT(1) Correspondence
• Shear Modes, Criticality and Extremal Black Holes
• How to Build the Thermofield Double State
• The Weak Gravity Conjecture and Effective Field Theory
• A comment on effective field theories of flux vacua
• Rescuing Single Field Inflation from the Swampland
• Do We Live in the Swampland?
• Avoiding the string swampland in single-field inflation: Excited initial states
• Constraining Neutrino Masses, the Cosmological Constant and BSM Physics from the Weak Gravity Conjecture
• Can Gravitational Instantons Really Constrain Axion Inflation?
• The de Sitter swampland conjecture and supersymmetric AdS vacua
• A note on Gauge Theories Coupled to Gravity
• Locality in Quantum Systems
• Quantum Corrections and the de Sitter Swampland Conjecture
• The dS swampland conjecture with the electroweak symmetry and QCD chiral symmetry breaking
• TASI Lectures on the Higher Spin - CFT duality
• An Axion-induced SM/MSSM Higgs Landscape and the Weak Gravity Conjecture
• On the weak gravity conjecture in string theory with broken supersymmetry
• A proof of the weak gravity conjecture
• Vacua Morghulis
• Constraining the EW Hierarchy from the Weak Gravity Conjecture
• Are tiny gauge couplings out of the Swampland?
• Mutual information and the F-theorem
• Towards a proof of the Weak Gravity Conjecture
• A Semiclassical, Entropic Proof of a Weak Gravity Conjecture
• Duality in generalized Ising models
• Semi-local Quantum Criticality and the Instability of Extremal Planar Horizons

Cited by in corpus (60)

• Lectures on the Swampland Program in String Compactifications
• The Weak Gravity Conjecture: A Review
• Repulsive Forces and the Weak Gravity Conjecture
• Festina Lente: EFT Constraints from Charged Black Hole Evaporation in de Sitter
• Modular Fluxes, Elliptic Genera, and Weak Gravity Conjectures in Four Dimensions
• Swampland Variations on a Theme by KKLT
• Gaugino condensation and small uplifts in KKLT
• Generalized Symmetry Breaking Scales and Weak Gravity Conjectures
• Tackling the SDC in AdS with CFTs
• Dimensional Reduction and (Anti) de Sitter Bounds
• Thermodynamics of 4D Dilatonic Black Holes and the Weak Gravity Conjecture
• The FL bound and its phenomenological implications
• Dark energy beyond quintessence: Constraints from the swampland
• Finiteness and the Swampland
• Modular Symmetries and the Swampland Conjectures
• A Strong Scalar Weak Gravity Conjecture and Some Implications
• Exploring The Holographic Swampland
• Duality and Axionic Weak Gravity
• de Sitter Cosmology on an expanding bubble
• On Higher-Spin Points and Infinite Distances in Conformal Manifolds
• Multi-field Inflation in High-Slope Potentials
• Bulk Reconstruction in Moduli Space Holography
• A universal formula for the density of states in theories with finite-group symmetry
• A New Spin on the Weak Gravity Conjecture
• Weak Gravity Conjecture, Black Hole Entropy, and Modular Invariance
• Scrambling and decoding the charged quantum information
• Scale-separated AdS${}_3$ vacua from $G_2$-orientifolds using bispinors
• Scale and quality of Peccei-Quinn symmetry and weak gravity conjectures
• Moduli Stabilisation and the Holographic Swampland
• The Weak Gravity Conjecture Requires the Existence of Exotic AdS Black Holes
• Corrections to Extremal Black Holes from Iyer-Wald Formalism
• Constraints on Early Dark Energy from the Axion Weak Gravity Conjecture
• Repulsive Black Holes and Higher-Derivatives
• Discrete Gauge Symmetries and the Weak Gravity Conjecture
• Brane nucleation instabilities in non-AdS/non-CFT
• From Rotating to Charged Black Holes and Back Again
• Classification of large N superconformal gauge theories with a dense spectrum
• Self-Binding Energies in AdS
• Holographic Perspectives On Models Of Moduli Stabilization In M-Theory
• Bootstrap bound on extremal Reissner-Nordström black hole in AdS
• A counterexample to the CFT convexity conjecture
• Dilatonic (Anti-)de Sitter Black Holes and Weak Gravity Conjecture
• Characters, quasinormal modes, and Schwinger pairs in $d{S}_2$ with flux
• A CFT Distance Conjecture
• Axionic Festina Lente
• Asymptotic safety, quantum gravity, and the swampland: a conceptual assessment
• Extremal Bifurcations of Rotating AdS${}_4$ Black Holes
• Holographic Dual of The Weak Gravity Conjecture
• Newton vs. Coulomb in AdS/CFT and the Weak Gravity Conjecture
• Assessing WGC Compatibility in ModMax Black Holes via Photon Spheres Analysis and WCCC Validation
• A Weak Gravity Theorem
• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme
• Higher-Derivative Corrections to Entropy and the Weak Gravity Conjecture in Anti-de Sitter Space
• Effective field theory in light of relative entropy
• Higher-Derivative Supergravity, AdS${}_4$ Holography, and Black Holes
• The correlation of WGC and Hydrodynamics bound with $R^4$ correction in the charged AdS${}_{d+2}$ black brane
• On Convexity of Charged Operators in CFTs and the Weak Gravity Conjecture
• De Sitter space constraints on brane tensions and couplings
• Extremal Instability for Topological Black Holes
• Holography, Supergravity, and the Weak Gravity Conjecture