Four coupled SYK models and Nearly AdS2 gravities: Phase Transitions in Traversable wormholes and in Bra-ket wormholes
|講演者||Dr. Tokiro Numasawa (The University of Tokyo)|
Wormholes are interesting and important objects in gravity. In particular, recently controllable examples of traversable wormholes are constructed. To understand these wormholes better, we study the two traversable wormhole configurations through the study of four coupled SYK models and nearly AdS2 gravities. In the SYK model side, we construct a model that couples two copies of two coupled SYK models. In the nearly AdS2 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 AdS2 gravity cases, through the double wick rotation, traversable wormholes are interpreted as bra-ket wormholes, which gives a connection between bra and ket vectors. 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 without 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.