A Tauberian theorem for the conformal bootstrap

DOI10.1007/JHEP12(2017)119zbMath1383.81253arXiv1709.00008MaRDI QIDQ1707783

Slava Rychkov, Jiaxin Qiao

Publication date: 3 April 2018

Published in: Journal of High Energy Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.00008

zbMATH Keywords

conformal field theoryconformal and W symmetry

Mathematics Subject Classification ID

Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Space-time singularities, cosmic censorship, etc. (83C75)

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Uses Software

• SDPB

Cites Work

• Unnamed Item
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• Conformal invariance in the long-range Ising model
• Bootstrapping the \(O\)(\(N\) ) vector models
• EPFL lectures on conformal field theory in \(D \geq 3\) dimensions
• Operator content of two-dimensional conformally invariant theories
• Cut-touching linear functionals in the conformal bootstrap
• The analytic bootstrap and AdS superhorizon locality
• Bounding scalar operator dimensions in 4D CFT
• Infinite conformal symmetry in two-dimensional quantum field theory
• Conformal partial waves and the operator product expansion
• Defects in conformal field theory
• Conformal bootstrap with slightly broken higher spin symmetry
• Precision islands in the Ising and \(O(N)\) models
• Analytic bounds and emergence of \(\mathrm{AdS}_{2}\) physics from the conformal bootstrap
• An algebraic approach to the analytic bootstrap
• The lightcone bootstrap and the spectrum of the 3d Ising CFT
• A line of CFTs: from generalized free fields to SYK
• Analyticity in spin in conformal theories
• The S-matrix bootstrap. I: QFT in AdS
• Crossing symmetry in alpha space
• Anomalous dimensions in the WF O(\(N\)) model with a monodromy line defect
• Extremal bootstrapping: go with the flow
• Solving the 3d Ising model with the conformal bootstrap. II: \(c\)-minimization and precise critical exponents
• Remarks on the convergence properties of the conformal block expansion
• Half-BPS Wilson loop and \(\mathrm{AdS}_{2}/\mathrm{CFT}_{1}\)
• Universal anomalous dimensions at large spin and large twist
• Analytic bootstrap at large spin
• Large spin systematics in CFT
• Tauberian Theory
• A scaling theory for the long-range to short-range crossover and an infrared duality
• Tauberian theorems in quantum field theory
• Conformal four point functions and the operator product expansion
• Glueball and meson propagators of any spin in large-\(N\) \textit{QCD}