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

## TL;DR

This paper investigates bulk reconstruction in the AdS$_3$/WCFT$_2$ correspondence, deriving a new bulk-boundary propagator and defining a bulk proto-scalar field using Virasoro-Kac-Moody symmetry, with two consistent approaches.

## Contribution

It introduces a novel bulk-boundary propagator and constructs the bulk proto-scalar field in AdS$_3$/WCFT$_2$ using symmetry principles, expanding holographic reconstruction methods.

## Key findings

- Derived a new bulk-boundary propagator for AdS$_3$/WCFT$_2$
- Constructed the bulk proto-scalar field via two symmetry-based methods
- Found the two approaches yield consistent bulk reconstruction results

## 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.