Dual gravities from entanglement entropy

TL;DR

This paper develops a holographic method to reconstruct dual gravity theories from entanglement entropy data, demonstrating both analytical and numerical approaches for undeformed and deformed CFTs.

Contribution

It introduces a rule-based approach to reconstruct dual gravity geometries from entanglement entropy, including analytical solutions and numerical methods for deformed theories.

Findings

Successfully derived 3D black hole geometry from 2D thermal entanglement entropy.

Reconstructed dual geometries analytically for undeformed CFTs using Abel transformation.

Numerically reconstructed dual gravity theories reveal RG flow properties like beta and c-functions.

Abstract

Applying a rule-based holographic method, we investigate the reconstruction of dual gravity theories from the quantum field theory (QFT) data, specifically entanglement entropy. We first derive a three-dimensional black hole geometry from the entanglement entropy of a two-dimensional thermal system. Using the reconstructed solution, we extract various thermodynamic quantities with small numerical errors. Moreover, we explore how to reconstruct the dual gravity theory beyond the geometry itself. For an undeformed conformal field theory (CFT), we show that the dual gravity theory can be constructed analytically from the analytic form of the entanglement entropy. In particular, we demonstrate how to reconstruct the analytic dual geometry by applying the Abel transformation. Finally, we investigate the numerical reconstruction of the dual gravity theory from numerical entanglement entropy data for a relevantly deformed CFT. After reconstructing the dual gravity, we show that additional information about the renormalization group (RG) flow, for instance, the $\b$-function and the $c$-function, can be extracted for the considered relevantly deformed CFT.