Expanding the Black Hole Interior: Partially Entangled Thermal States in SYK

Understand

We introduce a family of partially entangled thermal states in the SYK model that interpolates between the thermo-field double state and a pure (product) state.

• The states are prepared by a euclidean path integral describing the evolution over two euclidean time segments separated by a local scaling operator $\mathcal{O}$.
• We argue that the holographic dual of this class of states consists of two black holes with their interior regions connected via a domain wall, described by the worldline of a massive particle.
• We compute the size of the interior region and the entanglement entropy as a function of the scale dimension of $\mathcal{O}$ and the temperature of each black hole.