Bulk reconstruction of AdS$_{d+1}$ metrics and developing kinematic space

TL;DR

This paper presents a method for reconstructing AdS$_{d+1}$ metrics from lightcone cuts, introduces a new kinematic space of minimal surfaces, and explores properties for bulk metric reconstruction.

Contribution

It develops a novel approach to determine the conformal factor in metric reconstruction and proposes a new kinematic space concept for higher dimensions.

Findings

Explicit reconstruction of AdS metrics from lightcone cuts.

Identification of causal information surfaces as minimal surfaces.

Proposal of a generalized kinematic space for $d>2$.

Abstract

The metrics of the global, Poincar\'e, and Rindler AdS$_{d+1}$ are explicitly reconstructed with given lightcone cuts. We first compute the metric up to a conformal factor with the lightcone cuts method introduced by Engelhardt and Horowitz. While a general prescription to determine the conformal factor is not known, we recover the factor by identifying the causal information surfaces from the lightcone cuts and finding that they are minimal. In addition, we propose a new type of kinematic space as the space of minimal surfaces in AdS$_{d+1}$, where a metric is introduced as a generalization of the case of $d=2$. This metric defines the set of bulk points, which is equivalent to that of lightcone cuts. Some other properties are also studied towards establishing a reconstruction procedure for general bulk metrics.