Entwinement and the emergence of spacetime

TL;DR

This paper introduces the concept of entwinement to capture fine-grained quantum correlations in holographic theories, enabling the reconstruction of spacetime regions inaccessible to traditional entanglement measures, with implications for understanding black hole interiors.

Contribution

It proposes entwinement as a new measure of quantum correlations that probes spacetime regions beyond the entanglement shadow in holography, especially in systems with gauged, internal degrees of freedom.

Findings

Entwinement relates to non-minimal geodesics in conical defect geometries.

Spatial entanglement reproduces spacetime geometry up to the defect.

Entwinement enables reconstruction of the interior geometry beyond the entanglement shadow.

Abstract

It is conventional to study the entanglement between spatial regions of a quantum field theory. However, in some systems entanglement can be dominated by "internal", possibly gauged, degrees of freedom that are not spatially organized, and that can give rise to gaps smaller than the inverse size of the system. In a holographic context, such small gaps are associated to the appearance of horizons and singularities in the dual spacetime. Here, we propose a concept of entwinement, which is intended to capture this fine structure of the wavefunction. Holographically, entwinement probes the entanglement shadow -- the region of spacetime not probed by the minimal surfaces that compute spatial entanglement in the dual field theory. We consider the simplest example of this scenario -- a 2d conformal field theory (CFT) that is dual to a conical defect in AdS3 space. Following our previous work, we show that spatial entanglement in the CFT reproduces spacetime geometry up to a finite distance from the conical defect. We then show that the interior geometry up to the defect can be reconstructed from entwinement that is sensitive to the discretely gauged, fractionated degrees of freedom of the CFT. Entwinement in the CFT is related to non-minimal geodesics in the conical defect geometry, suggesting a potential quantum information theoretic meaning for these objects in a holographic context. These results may be relevant for the reconstruction of black hole interiors from a dual field theory.