Holographic Reconstruction of Gravitational Perturbations in AdS/CFT and Implications for Celestial Conformal Field Theory

TL;DR

This paper advances holographic reconstruction techniques for gravitational perturbations in AdS/CFT, emphasizing Lorentzian methods and exploring implications for celestial conformal field theory and flat spacetime limits.

Contribution

It generalizes holographic reconstruction to gravitational perturbations with a Lorentzian approach and links it to celestial CFT via BMS charges.

Findings

Reproduces and extends scalar field reconstruction results.

Formulates gravitational perturbation mapping as a light-like integral of stress tensor.

Connects celestial CFT with large central charge limits of 3d CFT.

Abstract

We begin by reexamining the holographic reconstruction of scalar fields in four-dimensional anti-de Sitter spacetime, adopting a purely Lorentzian signature derivation, reproducing earlier results of HKLL and generalizing to arbitrary boundary metrics. The approach is extended to gravitational perturbations, focussing on perturbations around $AdS_{4}$ and show that the mapping can be formulated as a purely light-like integral of the conformal field theory stress energy tensor. An example is considered of relevance to the flat spacetime limit with nontrivial BMS charges turned on, potentially providing a quantum field theory definition of celestial CFT as a large central charge limit of a 3d CFT.