Rindler Bulk Reconstruction and Subregion Duality in AdS/CFT

TL;DR

This paper investigates the limitations of AdS-Rindler reconstruction in holography, revealing tachyonic modes that challenge causality, unitarity, and the validity of subregion duality in the AdS/CFT correspondence.

Contribution

It demonstrates the presence of tachyonic modes in AdS-Rindler reconstruction and their implications for causality, unitarity, and the UV sensitivity of the mode expansion.

Findings

Tachyonic modes invalidate subregion duality in AdS-Rindler reconstruction.

Tachyonic modes connect to high-energy modes and quantum gravity effects.

Mode expansion sensitivity to UV limit due to null geodesics.

Abstract

In this paper, we study the AdS-Rindler reconstruction. The CFT operators naively given by the holographic dictionary for the AdS-Rindler reconstruction contain tachyonic modes, which are inconsistent with the causality and unitarity of the CFT. Therefore, the subregion duality and the entanglement wedge reconstruction do not hold. We also find that the tachyonic modes in the AdS-Rindler patch lead to arbitrary high-energy or trans-Planckian modes in the global AdS. It means that the mode expansion of the Rindler patch is sensitive to the UV limit of the theory, that is, quantum gravity. In addition, the tachyonic modes are related to the existence of null geodesics connecting the past and future horizons.