# Extension of the HKLL bulk reconstruction for small $\Delta$

## TL;DR

This paper extends the HKLL bulk reconstruction method for scalar fields in Lorentzian AdS spacetime to include smaller conformal dimensions, emphasizing the importance of the Green's function's singular part for accurate reconstruction.

## Contribution

It introduces modifications to the HKLL reconstruction for a broader range of conformal dimensions, highlighting the role of space-like Green's functions and their singular parts.

## Key findings

- Reconstruction valid for smaller conformal dimensions
- Inclusion of the Green's function's singular part improves accuracy
- Simplified results for integer conformal dimensions below original range

## Abstract

We re-analyse the bulk reconstruction for a scalar field in Lorentzian AdS spacetime, both for the case of even and odd dimensions, for an extended range of conformal dimensions where the original HKLL reconstruction has to be modified. We also discuss the use of space-like Green's functions in the bulk reconstruction. We demonstrate that in the extended range also the singular part of the Green's function, omitted in the original papers, has be included. The results are particularly simple and physically interesting for integer conformal dimensions below the range considered in the original HKLL papers.