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arXiv · 1811.09375

Comments on spinning OPE blocks in AdS$_{3}$/CFT$_{2}$

Suchetan Das
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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.

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Suchetan Das. 2018-11-23. Comments on spinning OPE blocks in AdS$_{3}$/CFT$_{2}$. https://doi.org/10.1016/j.physletb.2019.03.058

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