Note on Bulk Reconstruction in AdS$_3$/WCFT$_2$

Abstract: The bulk reconstructions in AdS/CFT and its cousins are essential to understand the holographic nature of quantum gravity. In this work, we try to study the bulk reconstruction in the AdS$_3$/WCFT$_2$ correspondence. After deriving the bulk-boundary propagator, which is different from the usual one in AdS/CFT, we define the bulk proto-scalar field by using the Virasoro-Kac-Moody symmetry in two different ways. One is to impose the bulk primary conditions on the field and construct the field algebraically. The other is to use the bulk-boundary vacuum OPE block, which can be read by applying the diffeomorphism preserving the CSS boundary conditions. Two approaches lead to consistent picture.