Going beyond ER=EPR in the SYK model

Berkooz, Micha; Brukner, Nadav; Ross, Simon F.; Watanabe, Masataka

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.

Citation

Berkooz, M., Brukner, N., Ross, S. F., & Watanabe, M. (2022). Going beyond ER=EPR in the SYK model. Journal of High Energy Physics, 2022(8), Article 51. https://doi.org/10.1007/jhep08%282022%29051

• Journal Article Type: Article
• Acceptance Date: Jun 24, 2022
• Online Publication Date: Aug 3, 2022
• Publication Date: 2022-08
• Deposit Date: Aug 5, 2022
• Publicly Available Date: Aug 5, 2022
• Journal: Journal of High Energy Physics
• Print ISSN: 1126-6708
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2022
• Issue: 8
• Article Number: 51
• DOI: https://doi.org/10.1007/jhep08%282022%29051