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.

arXiv comment36 pages + appendices; 6 figures. v2: Minor changes, expanded discussion in appendix B

References in corpus (141)

• Quantum entanglement
• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Microscopic Origin of the Bekenstein-Hawking Entropy
• Area laws for the entanglement entropy - a review
• Entanglement entropy and conformal field theory
• Eternal Black Holes in AdS
• Charged AdS Black Holes and Catastrophic Holography
• The String Landscape, Black Holes and Gravity as the Weakest Force
• Cool horizons for entangled black holes
• On the Geometry of the String Landscape and the Swampland
• Generalized gravitational entropy
• An Area Law for One Dimensional Quantum Systems
• Breaking an Abelian gauge symmetry near a black hole horizon
• Symmetries and Strings in Field Theory and Gravity
• Quantum corrections to holographic entanglement entropy
• Holography, Thermodynamics and Fluctuations of Charged AdS Black Holes
• Time Evolution of Entanglement Entropy from Black Hole Interiors
• Distance and de Sitter Conjectures on the Swampland
• Holography from Conformal Field Theory
• Area laws in quantum systems: mutual information and correlations
• Spectral Gap and Exponential Decay of Correlations
• On the Cosmological Implications of the String Swampland
• Anti-de Sitter Fragmentation
• Entanglement entropy of black holes
• GRAVITY AND GLOBAL SYMMETRIES
• Emergent quantum criticality, Fermi surfaces, and AdS2
• The String Landscape and the Swampland
• The AdS/CFT Correspondence and a New Positive Energy Conjecture for General Relativity
• Black Hole Entropy Function, Attractors and Precision Counting of Microstates
• De Sitter Space and the Swampland
• Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models
• The Ryu-Takayanagi Formula from Quantum Error Correction
• Aspects of generic entanglement
• What if string theory has no de Sitter vacua?
• Infinite Distances in Field Space and Massless Towers of States
• Remarks on entanglement entropy for gauge fields
• Holographic Entanglement Entropy
• EPFL Lectures on Conformal Field Theory in D>= 3 Dimensions
• $\mathcal{N}=1$ supersymmetric indices and the four-dimensional A-model
• Holographic quantum matter
• Wormholes, Emergent Gauge Fields, and the Weak Gravity Conjecture
• Emergent Spacetime and Holographic CFTs
• Tensionless Strings and the Weak Gravity Conjecture
• Naturalness and the Weak Gravity Conjecture
• Super-Planckian Spatial Field Variations and Quantum Gravity
• The landscape, the swampland and the era of precision cosmology
• The Weak Gravity Conjecture and Scalar Fields
• Constraints on symmetry from holography
• Evidence for a Lattice Weak Gravity Conjecture
• On the de Sitter swampland criterion
• AdS${}_2$ holography and the SYK model
• Transplanckian axions !?
• Emergence and the Swampland Conjectures
• Sharpening the Weak Gravity Conjecture with Dimensional Reduction
• Landscape of superconducting membranes
• On The Entanglement Entropy For Gauge Theories
• A Stringy Test of the Scalar Weak Gravity Conjecture
• Weak Gravity Conjecture from Unitarity and Causality
• The Weak Gravity Conjecture in three dimensions
• The string swampland constraints require multi-field inflation
• Proof of the Weak Gravity Conjecture from Black Hole Entropy
• A Tower Weak Gravity Conjecture from Infrared Consistency
• Infinite Distance Networks in Field Space and Charge Orbits
• Exponential Decay of Correlations Implies Area Law
• Natural Inflation and Quantum Gravity
• De Sitter vs Quintessence in String Theory
• The $\mathcal{N}=2$ superconformal bootstrap
• Planckian Axions and the Weak Gravity Conjecture
• The dual superconformal theory for Lpqr manifolds
• Dark Energy in the Swampland
• The dS swampland conjecture and the Higgs potential
• The Weak Gravity Conjecture and Emergence from an Ultraviolet Cutoff
• An area law for entanglement from exponential decay of correlations
• Weak Gravity Strongly Constrains Large-Field Axion Inflation
• Models of AdS_2 Backreaction and Holography
• Power law violation of the area law in quantum spin chains
• A note on Inflation and the Swampland
• On the Possibility of Large Axion Moduli Spaces
• Some Results on Mutual Information of Disjoint Regions in Higher Dimensions
• Black hole determinants and quasinormal modes
• Entropy Function and AdS(2)/CFT(1) Correspondence
• Supersymmetry Breaking by Fluxes
• Semi-local quantum liquids
• Shear Modes, Criticality and Extremal Black Holes
• de Sitter Swampland, $H_0$ tension & observation
• On Axionic Field Ranges, Loopholes and the Weak Gravity Conjecture
• Relaxion Monodromy and the Weak Gravity Conjecture
• Conformal Symmetry Breaking and Thermodynamics of Near-Extremal Black Holes
• Holographic Mutual Information at Finite Temperature
• How to Build the Thermofield Double State
• Schwinger pair production in AdS2
• Weak Gravity Conjecture in AdS/CFT
• The Weak Gravity Conjecture and Effective Field Theory
• A comment on effective field theories of flux vacua
• The String Landscape, the Swampland, and the Missing Corner
• Eternal Inflation and Swampland Conjectures
• Do We Live in the Swampland?
• Rescuing Single Field Inflation from the Swampland
• New constraints on classical de Sitter: flirting with 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
• Scalar Fields, Hierarchical UV/IR Mixing and The Weak Gravity Conjecture
• Large-Field Inflation with Multiple Axions and the Weak Gravity Conjecture
• Warping the Weak Gravity Conjecture
• The superradiant instability regime of the spinning Kerr black hole
• Can Gravitational Instantons Really Constrain Axion Inflation?
• The de Sitter swampland conjecture and supersymmetric AdS vacua
• Trouble For Remnants
• A note on Gauge Theories Coupled to Gravity
• de Sitter extrema and the swampland
• Locality in Quantum Systems
• Quantum Corrections and the de Sitter Swampland Conjecture
• Linearity of Holographic Entanglement Entropy
• Complexity is Simple
• The dS swampland conjecture with the electroweak symmetry and QCD chiral symmetry breaking
• A Chern-Simons Pandemic
• TASI Lectures on the Higher Spin - CFT duality
• What is the Magnetic Weak Gravity Conjecture for Axions?
• Ground State Entanglement in One Dimensional Translationally Invariant Quantum Systems
• An Axion-induced SM/MSSM Higgs Landscape and the Weak Gravity Conjecture
• Mass Hierarchies and Dynamical Field Range
• Aspects of Holographic Entanglement at Finite Temperature and Chemical Potential
• The Fundamental Need for a SM Higgs and the Weak Gravity Conjecture
• On the weak gravity conjecture in string theory with broken supersymmetry
• Lattice Gauge Theories and Spin Models
• A note on the extensivity of the holographic entanglement entropy
• A proof of the weak gravity conjecture
• AdS-phobia, the WGC, the Standard Model and Supersymmetry
• Entanglement area law from specific heat capacity
• Vacua Morghulis
• Entanglement and Correlations near Extremality: CFTs dual to Reissner-Nordström AdS${}_5$
• Constraining the EW Hierarchy from the Weak Gravity Conjecture
• Mutual information and the F-theorem
• Are tiny gauge couplings out of the Swampland?
• Towards a proof of the Weak Gravity Conjecture
• A Comment on Continuous Spin Representations of the Poincaré Group and Perturbative String Theory
• A Semiclassical, Entropic Proof of a Weak Gravity Conjecture
• Lattice Gauge Theory - A short Primer
• Black branes in AdS: BPS bounds and asymptotic charges
• Duality in generalized Ising models
• Semi-local Quantum Criticality and the Instability of Extremal Planar Horizons

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• Scale and quality of Peccei-Quinn symmetry and weak gravity conjectures
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• 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
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• 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