Berry phases, wormholes and factorization in AdS/CFT

Abstract

For two-dimensional holographic CFTs, we demonstrate the role of Berry phases for relating the non-factorization of the Hilbert space to the presence of wormholes. The wormholes are characterized by a non-exact symplectic form that gives rise to the Berry phase. For wormholes connecting two spacelike regions in gravitational spacetimes, we find that the non-exactness is linked to a variable appearing in the phase space of the boundary CFT. This variable corresponds to a loop integral in the bulk. Through this loop integral, non-factorization becomes apparent in the dual entangled CFTs. Furthermore, we classify Berry phases in holographic CFTs based on the type of dual bulk diffeomorphism involved. We distinguish between Virasoro, gauge and modular Berry phases, each corresponding to a spacetime wormhole geometry in the bulk. Using kinematic space, we extend a relation between the modular Hamiltonian and the Berry curvature to the finite temperature case. We find that the Berry curvature, given by the Crofton form, characterizes the topological transition of the entanglement entropy in presence of a black hole.

Replicas, averaging and factorization in the IIB matrix model

“…The main outcome of our adventure can be summarized in the following way: (1) the restoration of factorization with n ≥ 4 replicas (2) the nonfactorization of the two-replica JHEP09(2022)136 system and the nontrivial factorization of the four-replica system for the noninteracting Dbranes (3) the trivial factorization for any number of replicas in interacting D-brane systems (4) the absence of self-averaging. On one hand, the restoration of factorization is overall in line with the previous results from the literature for the SYK model [12,15,16,23,25] and the general expectation that our intuition should somehow survive so that the thermodynamic potentials of multiple independent copies of any system should just add up (i.e. the partition functions should just multiply).…”

“…In [20][21][22] the traversable spatial ("Lorentzian") wormholes have also been related to field theories averaged over the states or over the operators, starting, as could be expected, from thermofield-dynamics (TFD)-like states. Some recent generalizations are found in [23][24][25][26] and in particular in [27], where the authors find that nonlocally interacting bulk branes in 2D gravity provide a mechanism which restores factorization in absence of any explicit disorder.…”

A universal approach to Krylov state and operator complexities

“…This non-locality is quantified through the symplectic structure in the bulk, which although can have local interpretation of time evolution with H + , are globally non-exact, thereby giving rise to the additional phases appearing in the generalized TFD states [32,33].…”

“…This can alternatively be attributed to a fundamentally non-factorized structure of the Hilbert space as well. In the context of the entanglement structure of a generic quantum system, this connection was discussed in [32,33].…”

Wormholes, geons, and the illusion of the tensor product

“…In [15] a model was built, where the factorization of the otherwise non-factorizable Hilbert space emerges at low energies. In the context of holographic theories a comprehensive analysis was carried out in the series of papers [16][17][18][19][20][21]. It was shown that in the presence of gravity the holographic theory 'sees' more degrees of freedom than naively expected, which suggests that the bulk Hilbert space is 'smaller' than naively expected.…”