Holographic de Sitter Geometry from Entanglement in Conformal Field Theory

TL;DR

This paper reveals that small entanglement perturbations in conformal field theories can be described by a Klein-Gordon equation in an emergent de Sitter space, linking entanglement structure to holographic geometry.

Contribution

It introduces a novel holographic framework where entanglement perturbations in CFTs correspond to scalar fields in an auxiliary de Sitter space, extending to theories with conserved charges.

Findings

Entanglement perturbations satisfy a Klein-Gordon equation in de Sitter space.

Emergent de Sitter geometry encodes entanglement structure in CFTs.

Additional conserved charges lead to multiple scalar fields in the de Sitter space.

Abstract

We demonstrate that for general conformal field theories (CFTs), the entanglement for small perturbations of the vacuum is organized in a novel holographic way. For spherical entangling regions in a constant time slice, perturbations in the entanglement entropy are solutions of a Klein-Gordon equation in an auxiliary de Sitter (dS) spacetime. The role of the emergent time-like direction in dS is played by the size of the entangling sphere. For CFTs with extra conserved charges, e.g., higher spin charges, we show that each charge gives rise to a separate dynamical scalar field in dS.