Thermal Conformal Blocks

Abstract

We study conformal blocks for thermal one-point-functions on the sphere in conformal field theories of general dimension. These thermal conformal blocks satisfy second order Casimir differential equations and have integral representations related to AdS Witten diagrams. We give an analytic formula for the scalar conformal block in terms of generalized hypergeometric functions. As an application, we deduce an asymptotic formula for the three-point coeffcients of primary operators in the limit where two of the operators are heavy.

arXiv comment39 pages, 2 figures, v2: added minor clarification and references

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Cited by in corpus (17)

• Proper time to the black hole singularity from thermal one-point functions
• Heavy Operators and Hydrodynamic Tails
• OPE statistics from higher-point crossing
• Thermalization in Large-N CFTs
• Holographic open quantum systems: Toy models and analytic properties of thermal correlators
• Thermal Stress Tensor Correlators, OPE and Holography
• Thermal correlation functions in CFT and factorization
• Holographic torus correlators of stress tensor in $Ad{S}_3/CF{T}_2$
• An embedding formalism for CFTs in general states on curved backgrounds
• More on Wilson toroidal networks and torus blocks
• Tidal excitation as mixing in thermal CFT
• Wilson lines construction of $\mathfrak{osp}(1|2)$ conformal blocks
• Conformal line defects at finite temperature
• Conformal Blocks in Two and Four Dimensions from Oscillator Representations
• Wilson lines construction of ${\mathfrak{sl}}_3$ toroidal conformal blocks
• Finite Temperature at Finite Places
• The thermal representation of conformal ladder integrals