Bound on asymptotics of magnitude of three point coefficients in 2D CFT

Abstract

We use methods inspired from complex Tauberian theorems to make progress in understanding the asymptotic behavior of the magnitude of heavy-light-heavy three point coefficients rigorously. The conditions and the precise sense of averaging, which can lead to exponential suppression of such coefficients are investigated. We derive various bounds for the typical average value of the magnitude of heavy-light-heavy three point coefficients and verify them numerically.

arXiv comment41 pages, many figures, v2: 43 pages, typos fixed, notation clarified, references and new graph added v3: refined argument and more precise numerics

References in corpus (20)

• Thermalization and its mechanism for generic isolated quantum systems
• Universal Spectrum of 2d Conformal Field Theory in the Large c Limit
• Does a single eigenstate encode the full Hamiltonian?
• A Universal Inequality for CFT and Quantum Gravity
• A Cardy Formula for Three-Point Coefficients: How the Black Hole Got its Spots
• Quantum Regge Trajectories and the Virasoro Analytic Bootstrap
• A tauberian theorem for the conformal bootstrap
• Modular Invariance, Tauberian Theorems, and Microcanonical Entropy
• Light Cone Bootstrap in General 2D CFTs and Entanglement from Light Cone Singularity
• Analytic Euclidean Bootstrap
• A Cardy formula for off-diagonal three-point coefficients; or, how the geometry behind the horizon gets disentangled
• Entanglement Entropy, OTOC and Bootstrap in 2D CFTs from Regge and Light Cone Limits of Multi-point Conformal Block
• Typicality and thermality in 2d CFT
• Constraints on Flavored 2d CFT Partition Functions
• Charged structure constants from modularity
• Modular Constraints on Conformal Field Theories with Currents
• Growing Extra Dimensions in AdS/CFT
• Thermal Correlation Functions of KdV Charges in 2D CFT
• Quantum corrections to the BTZ black hole extremality bound from the conformal bootstrap
• Light-state Dominance from the Conformal Bootstrap

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• Bounds on the density of states and the spectral gap in CFT${}_2$
• Twist accumulation in conformal field theory. A rigorous approach to the lightcone bootstrap
• Universality in asymptotic bounds and its saturation in $2$D CFT
• Multiboundary wormholes and OPE statistics
• Hamiltonian truncation in Anti-de Sitter spacetime
• Universal Dynamics of Heavy Operators in Boundary CFT${}_2$
• Hartle-Hawking state and its factorization in 3d gravity
• Aspects of the S transformation Bootstrap