Going beyond ER=EPR in the SYK model

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.

References in corpus (4)

• Entanglement entropy in three dimensional gravity
• Black Holes, Entanglement and Random Matrices
• Canonical Purification of Evaporating Black Holes
• Seeing behind black hole horizons in SYK

Cited by in corpus (10)

• Pseudo Entropy in dS/CFT and Time-like Entanglement Entropy
• Timelike entanglement entropy
• Krylov complexity in large-$q$ and double-scaled SYK model
• SVD Entanglement Entropy
• Parisi's hypercube, Fock-space fluxes, and the microscopics of near-AdS${}_2$/near-CFT${}_1$ duality
• SYK Model with global symmetries in the double scaling limit
• Spacetime topology from holographic entanglement
• On perturbation around closed exclusion processes
• Grothendieck's point of view and complexity in the black hole paradox
• Replicas, averaging and factorization in the IIB matrix model