Hilbert space factorization of eternal black holes in AdS/CFT

The talk will be devoted to the Hilbert space factorization problem in the context of AdS/CFT-correspondence. The essence of the problem is in the fact that, according to the AdS/CFT-correspondence, the bulk theory on the eternal black hole background is dual to two copies of the conformal field theory (CFT) which live on the two asymptotic boundaries. Thus, the Hilbert space of the dual CFT has the explicit tensor product structure, which leads to factorization of a wide class of observables. However, from the bulk gravity point of view, where typical states are described by connected asymptotically AdS geometries with two boundaries, this tensor product structure is not explicitly evident. In the talk I will discuss the recent advancements in understanding the Hilbert space structure of AdS gravity at the semiclassical level, and how these ideas help resolve the factorization problem in the bulk.