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.

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

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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