Baby Universes from Thermal Pure States in SYK

Abstract

We construct a simple two-dimensional holographic model of a closed "baby" universe. The baby universe spacetime originates from the black hole interior in Jackiw-Teitelboim (JT) gravity. The holographic description is a low-temperature thermal pure state of two Sachdev-Ye-Kitaev (SYK) models. The construction of the state relies on the insertion of a heavy matter operator, which supports the baby universe, together with a first-order thermal phase transition between a black hole phase and an empty Anti de Sitter (AdS) phase. For the transition, we employ a version of the Maldacena-Qi phase transition of two coupled SYK systems. The bulk entanglement between the AdS region and the baby universe remains O(N) below the transition, owing to the large number of light bulk fields. This entanglement admits a definition through coarse-graining over SYK couplings.

Figures (4)

• Figure 1: Top: Semiclassical state of a two-sided black hole with a heavy matter particle in the black hole interior. Evolving the state with a strong enough MQ coupling (orange) allows us to reconstruct the interior. Bottom: The Euclidean manifold $\Sigma_{\rm d}$ preparing the semiclassical state on the gray slice. The geodesic of renormalized length $\ell$ is shown in dark blue.
• Figure 2: Top: Semiclassical state of an empty wormhole $\mathsf{a}$ with large bulk entanglement to a baby universe $\mathsf{c}$. Bottom: The Euclidean manifold $\Sigma_{\rm h}$ preparing the semiclassical state on the gray slice. The moduli of the handle are stabilized by the heavy particle and by the MQ interaction.
• Figure 3: Probability distribution of $c_0[J]$ for a fixed operator $\mathcal{O}_\Delta=\psi_{1}\cdots\psi_{8}$ over $10^5$ realizations of the SYK couplings. We take $\mathcal{J}=1$. The global phase of the MQ ground state $\ket{0}$ is fixed by the condition $\langle 0|I\rangle>0$, and the analysis is restricted to the $Q\equiv 0~(\mathrm{mod}\,4)$ subspace. In (a) we fix $N$ and vary $\mu$, while in (b) we fix $\mu$ and vary $N$. We show only the absolute value; we find that the sign is uniformly distributed.
• Figure 4: Uniformization of the handle. The blue lines correspond to minimal length geodesics between the boundary points.