Going beyond ER=EPR in the SYK model

TL;DR

This paper explores generalized density matrices in the SYK model to better understand the conditions under which semiclassical wormholes form, extending beyond entanglement-based criteria.

Contribution

It introduces a new framework for characterizing wormholes using specific density matrices, providing a finer criterion for semiclassicality beyond entanglement.

Findings

Different density matrices correspond to distinct semiclassical profiles.

The length of the wormhole encodes the degree of correlation erosion.

The SYK model captures wormhole features via chord diagrams.

Abstract

We discuss generalizations of the TFD to a density matrix on the doubled Hilbert space. We suggest that a semiclassical wormhole corresponds to a certain class of such density matrices, and specify how they are constructed. Different semi-classical profiles correspond to different non-overlapping density matrices. We show that this language allows for a finer criteria for when the wormhole is semiclassical, which goes beyond entanglement. Our main tool is the SYK model. We focus on the simplest class of such density matrices, in a scaling limit where the ER bridge is captured by chords going from one space to another, encoding correlations in the microscopic Hamiltonian. The length of the wormhole simply encodes the extent these correlations are eroded when flowing from one side to the other.