The Weak Gravity Conjecture in three dimensions

Abstract

We study weakly coupled $U(1)$ theories in $Ad{S}_3$, their associated charged BTZ solutions, and their charged spectra. We find that modular invariance of the holographic dual two-dimensional CFT and compactness of the gauge group together imply the existence of charged operators with conformal dimension significantly below the black hole threshold. We regard this as a form of the Weak Gravity Conjecture (WGC) in three dimensions. We also explore the constraints posed by modular invariance on a particular discrete ${\mathbb{Z}}_N$ symmetry which arises in our discussion. In this case, modular invariance does not guarantee the existence of light ${\mathbb{Z}}_N$-charged states. We also highlight the differences between our discussion and the usual heuristic arguments for the WGC based on black hole remnants.

44 pages

References in corpus (41)

• The Black Hole in Three Dimensional Space Time
• The String Landscape, Black Holes and Gravity as the Weakest Force
• The (2+1)-Dimensional Black Hole
• Spacetime Instanton Corrections in 4D String Vacua - The Seesaw Mechanism for D-Brane Models
• Neutrino Majorana Masses from String Theory Instanton Effects
• Conformal Field Theory, (2+1)-Dimensional Gravity, and the BTZ Black Hole
• Wormholes, Emergent Gauge Fields, and the Weak Gravity Conjecture
• R^4 Couplings in M and Type II Theories
• Naturalness and the Weak Gravity Conjecture
• Stringy Instantons and Quiver Gauge Theories
• Quantum Hair on Black Holes
• Transplanckian axions !?
• A Universal Inequality for CFT and Quantum Gravity
• Sharpening the Weak Gravity Conjecture with Dimensional Reduction
• Backreacted Axion Field Ranges in String Theory
• Natural Inflation and Quantum Gravity
• Planckian Axions and the Weak Gravity Conjecture
• The $\mathcal{N}=2$ superconformal bootstrap
• Poincare Series, 3D Gravity and CFT Spectroscopy
• Weak Gravity Strongly Constrains Large-Field Axion Inflation
• On the Possibility of Large Axion Moduli Spaces
• Discrete gauge symmetries in D-brane models
• Relaxion Monodromy and the Weak Gravity Conjecture
• On Axionic Field Ranges, Loopholes and the Weak Gravity Conjecture
• Universal Bounds on Charged States in 2d CFT and 3d Gravity
• Evidence for an Electrifying Violation of Cosmic Censorship
• Chiral anomalies and AdS/CMT in two dimensions
• Large-Field Inflation with Multiple Axions and the Weak Gravity Conjecture
• Axion Monodromy and the Weak Gravity Conjecture
• Exact Results for the BTZ Black Hole
• Warping the Weak Gravity Conjecture
• Modulated Natural Inflation
• Fake Supersymmetry and Extremal Black Holes
• Hawking-Page phase transition in BTZ black hole revisited
• A note on Gauge Theories Coupled to Gravity
• Bounds for State Degeneracies in 2D Conformal Field Theory
• Phase transition between the BTZ black hole and AdS space
• Aligned natural inflation with modulations
• Subleading Effects and the Field Range in Axion Inflation
• The 2+1 charged black hole in topologically massive Electrodynamics
• Black Hole Meiosis

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