We compute the entanglement entropy of a discretized scalar field in the fixed spacetime background of an evolving wormhole. Evolving wormholes are a class of time dependent and spherically symmetric wormhole geometries. In both expanding and contracting models, we find dynamically generated entanglement. Asymptotically far from the wormhole throat, the entanglement entropy is well described by the leading term in the area law, although its coefficient can depend sensitively on the value of the UV cutoff. As the UV cutoff is decreased, the coefficient becomes progressively less sensitive to the cutoff, providing numerical evidence that it approaches a cutoff-independent value in the continuum limit. Near the throat, we find a double-dip structure in the entanglement entropy which cannot be described by the leading and logarithmic contributions to the area law.
Four coupled SYK models and Nearly AdS
2 gravities: Phase Transitions in Traversable wormholes and in Bra-ket wormholes
We study four coupled 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 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.
Maldacena and Susskind have proposed a correspondence between wormholes and entanglement, dubbed ER=EPR. We study this in the context of three-dimensional topological quantum field theory (TQFT), where we show that the formation of a wormhole is the same process as creating a particle–antiparticle pair. A key feature of the ER=EPR proposal is that certain apparently entangled degrees of freedom turn out to be the same. We name this phenomenon ‘fake entanglement’, and show how it arises in our TQFT model.