CFT reconstruction of local bulk operators in half-Minkowski space

TL;DR

This paper develops a holographic reconstruction method for massless fields in half-Minkowski space using a Weyl transformation and HKLL smearing functions, extending AdS/CFT techniques to flat spacetime.

Contribution

It introduces a new holographic map that reconstructs local bulk operators in half-Minkowski space from boundary CFT operators, generalizing existing AdS/CFT methods.

Findings

Reconstructed scalar fields up to two-point functions.

Reconstructed Maxwell and spin-2 fields at the one-point function level.

Discussed potential generalizations to higher dimensions and full Minkowski space.

Abstract

We construct a holographic map that reconstructs massless fields (scalars, Maxwell field \& Fierz-Pauli field) in half-Minkowski spacetime in $d+1$ dimensions terms of smeared primary operators in a large $N$ factorizable CFT in $\mathbb{R}^{d-1,1}$ spacetime dimensions. This map is based on a Weyl (rescaling) transformation from the Poincar\'e wedge of AdS to the Minkowski half-space; and on the HKLL smearing function, which reconstructs local bulk operators in the Poincar\'e AdS in terms of smeared operators on the conformal boundary of the Poincar\'e wedge. The massless scalar field is reconstructed up to the level of two-point functions, while the Maxwell field and massless spin-2 fields are reconstructed at the level of the one-point function. We also discuss potential ways the map can be generalized to higher dimensions, and to the full Minkowski space.