Comments on spinning OPE blocks in AdS3/CFT2

We extend the work of [48], [49], to obtain an integral expression of OPE blocks for spinning primaries in CFT2. We observe, when the OPE blocks are made out of conserved spinning primaries, the integral becomes a product of two copies of weighted AdS2 fields, smeared along geodesics. In this way, conserved current OPE blocks in CFT2 have a different representation in terms of AdS2 geodesic operators, in stead of viewing them as AdS3 geodesic operators. We also show, how this representation can be related to AdS3 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 AdS2 Geodesic Witten diagrams.