Four coupled SYK models and nearly AdS2 gravities: phase transitions in traversable wormholes and in bra-ket wormholes

We study four coupled Sachdev-Ye-Kitaev (SYK) models and nearly AdS(2) gravities. In the SYK model side, we construct a model that couples two copies of two coupled SYK models. In nearly AdS(2) gravity side, we entangle matter fields in two copies of traversable wormholes. In both cases, the systems show first order phase transitions at zero temperature by changing couplings, which is understood as the exchange of traversable wormhole configurations. In nearly AdS(2) gravity cases, by exchanging the role of space and time the wormholes are interpreted as bra-ket wormholes. In Lorentzian signature, these bra-ket wormholes lead to two closed universes that are entangled with each other as well as matter fields in the flat space where we do not have dynamical gravity. We study the effect of projection or entangling operation for matters on flat spaces and they cause phase transitions in bra-ket wormholes, which leads to the pair annihilation of closed universes. Using these bra-ket wormholes, we discuss the way to embed states in 2D holographic CFTs into Hilbert space of many 2D free fields.

Automated summary

This article studies coupled Sachdev-Ye-Kitaev (SYK) models and nearly AdS(2) gravities. By constructing models and entangling matter fields, the authors show the phenomenon of first order phase transitions at zero temperature under different couplings. The results of the study demonstrate that the exchange of wormholes plays an important role, and in Lorentzian signature, bra-ket wormholes lead to two entangled closed universes.