A tauberian theorem for the conformal bootstrap

Abstract

For expansions in one-dimensional conformal blocks, we provide a rigorous link between the asymptotics of the spectral density of exchanged primaries and the leading singularity in the crossed channel. Our result has a direct application to systems of SL(2,R)-invariant correlators (also known as 1d CFTs). It also puts on solid ground a part of the lightcone bootstrap analysis of the spectrum of operators of high spin and bounded twist in CFTs in d>2. In addition, a similar argument controls the spectral density asymptotics in large N gauge theories.

36pp; v2: refs and comments added, misprints corrected

References in corpus (3)

• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
• Bootstrapping Mixed Correlators in the 3D Ising Model

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• A Crossing-Symmetric OPE Inversion Formula
• Analytic Bootstrap in 2D Boundary Conformal Field Theory: Towards Braneworld Holography
• Higher-Dimensional Symmetry of AdS${}_2\times$S${}^2$ Correlators
• The Inversion Formula and 6j Symbol for 3d Fermions
• Universal Dynamics in Non-Orientable CFT${}_2$
• Analytic Studies of Fermions in the Conformal Bootstrap