IAS Quantum Aspects of Black Holes Group Meeting

Abstract: I will discuss a geometric approach to the factorization puzzle that involves coadjoint orbits and Berry phases. The mathematical formalism introduced is applied both to quantum mechanics examples and to AdS/CFT.  It is shown how the presence of a geometric phase determines the type of von Neumann algebra. The examples considered include two-sided black holes in AdS space, as well as two coupled spins and a chain of Majorana fermions.  Moreover, the generalized TFD states used for defining a Berry connection provide an explicit example for how non-perturbative corrections to the gravitational path integral reduce the Hilbert space size, leading to a type I von Neumann algebra. I will discuss lessons from these examples for the relation between geometry and entanglement in general.

Based on 2202.11717, 2306.00055, 2401.04764 and work in progress