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

Suchetan Das

doi:10.1016/j.physletb.2019.03.058

paper

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

arXiv:1811.09375 · doi:10.1016/j.physletb.2019.03.058

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.

Same as published version with one extra appendix is added

Comments on spinning OPE blocks in AdS3​/CFT2​

Abstract

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