Dimensional reduction for conformal blocks

2016/04/29 by Matthijs Hogervorst · 2 citations
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Conformal anomaly #Conformal field theory #Conformal map #Conformal symmetry #Generalized hypergeometric function #Geometry #Hypergeometric function #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Physics #Primary field #Pure mathematics #Reduction (mathematics) #hep-th

paper · pdf · doi:10.1007/jhep09(2016)017

12 pages, 1 figure

arxiv created 2016/04/29 · openalex publication_date 2016/09/01 · arxiv updated 2016/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We consider the dimensional reduction of a CFT, breaking multiplets of the d-dimensional conformal group SO(d + 1, 1) up into multiplets of SO(d, 1). This leads to an expansion of d-dimensional conformal blocks in terms of blocks in d − 1 dimensions. In particular, we obtain a formula for 3d conformal blocks as an infinite sum over 2 F 1 hypergeometric functions with closed-form coefficients.

Citations

• D-independent representation of Conformal Field Theories in D dimensions via transformation to auxiliary Dual Resonance Models. Scalar amplitudes
• Conformal Partial Waves: Further Mathematical Results
• Conformal partial waves and the operator product expansion
• Solving the 3d Ising Model with the Conformal Bootstrap II. c c -Minimization and Precise Critical Exponents
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• Bounding scalar operator dimensions in 4D CFT
• Bootstrapping mixed correlators in the 3D Ising model
• TASI Lectures on the Conformal Bootstrap
• A proof of the conformal collider bounds
• An Algebraic Approach to the Analytic Bootstrap

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