Comments on spinning OPE blocks in AdS${}_3$/CFT${}_2$

Abstract

We extend the work of \cite{Ferrara:1971vh},\cite{Ferrara:1973vz}, to obtain an integral expression of OPE blocks for spinning primaries in CFT${}_2$. We observe, when the OPE blocks are made out of conserved spinning primaries, the integral becomes a product of two copies of weighted AdS${}_2$ fields, smeared along geodesics. In this way, conserved current OPE blocks in CFT${}_2$ have a different representation in terms of AdS${}_2$ geodesic operators, in stead of viewing them as AdS${}_3$ geodesic operators. We also show, how this representation can be related to AdS${}_3$ massless higher spin fields through HKLL bulk field reconstruction. Using this picture, we consistently obtain the closed form expression of four point spinning conformal block as a product of two AdS${}_2$ Geodesic Witten diagrams.

arXiv commentSame as published version with one extra appendix is added

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• Late-time correlation functions in dS${}_3$/CFT${}_2$ correspondence
• Spectrum of Modular Hamiltonian in the Vacuum and Excited States
• The gravity dual of Lorentzian OPE blocks
• Virasoro algebras, kinematic space and the spectrum of modular Hamiltonians in CFT${}_2$
• Quantum Information Approaches to Quantum Gravity