Dimensional Reduction for Conformal Blocks

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 2F1 hypergeometric functions with closed-form coefficients.

12 pages, 1 figure

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Cited by in corpus (37)

• The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
• A Mellin space approach to the conformal bootstrap
• Dispersive CFT Sum Rules
• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
• Spinning Witten Diagrams
• Mellin space bootstrap for global symmetry
• Simplifying large spin bootstrap in Mellin space
• The Lorentzian inversion formula and the spectrum of the 3d O(2) CFT
• Anomalous Dimensions from Crossing Kernels
• Dispersion relations and exact bounds on CFT correlators
• Thermal Conformal Blocks
• Random Field Ising Model and Parisi-Sourlas Supersymmetry I. Supersymmetric CFT
• AdS${}_4$/CFT${}_3$ for Unprotected Operators
• Twist accumulation in conformal field theory. A rigorous approach to the lightcone bootstrap
• Towards Feynman rules for conformal blocks
• de Sitter swampland bound in the Dirac-Born-Infeld inflation model
• Towards a Bootstrap approach to higher orders of epsilon expansion
• Scalar Blocks as Gravitational Wilson Networks
• Celestial Yang-Mills Amplitudes and D=4 Conformal Blocks
• Quantum Integrable Systems from Conformal Blocks
• Closed-form expression for cross-channel conformal blocks near the lightcone
• Spinning correlators in $\mathcal{N}=2$ SCFTs: Superspace and AdS amplitudes
• Regge trajectories for the (2,0) theories
• Dimensional reduction of higher-point conformal blocks
• Conformal partial waves in momentum space
• Lightcone expansions of conformal blocks in closed form
• On Conformal Block, Crossing Kernel and Multi-variable Hypergeometric Functions
• More Analytic Bootstrap: Nonperturbative Effects and Fermions
• The Inversion Formula and 6j Symbol for 3d Fermions
• Applications of Alpha Space
• Factorized lightcone expansion of conformal blocks
• Theorems for the Lightcone Bootstrap
• General Bootstrap Equations in 4D CFTs
• How to Succeed at Witten Diagram Recursions without Really Trying
• Exact 3D Conformal Blocks from Fractional Calculus
• Analytic Studies of Fermions in the Conformal Bootstrap
• Critical Three-Dimensional Ising Model on Spheriods from the Conformal Bootstrap