Deconstructing the Wormhole: Factorization, Entanglement and Decoherence

We study the role of ensemble averaging in holography by exploring the relation between the universal late time behavior of the spectral form factor and the second Renyi entropy of a thermal mixed state of the doubled system. Both quantities receive contributions from wormhole saddle-points: in the former case they lead to non-factorization while in the latter context they quantify decoherence due to the interaction with an environment. Our reasoning indicates that the space-time continuity responsible for non-factorization and space-time continuity through entanglement are in direct competition with each other. In an accompanying paper, we examine this dual relationship in a general class of 1D quantum systems with the help of a simple geometric path integral prescription.