Berry phases, wormholes and factorization in AdS/CFT

TL;DR

This paper explores how Berry phases relate to wormholes and non-factorization in AdS/CFT, revealing topological transitions in entanglement entropy and classifying Berry phases by their bulk diffeomorphisms.

Contribution

It introduces a framework linking Berry phases to wormhole geometries and non-factorization in holographic CFTs, extending the understanding of entanglement and topology in AdS/CFT.

Findings

Berry phases correspond to different bulk diffeomorphisms.

Non-factorization linked to a boundary phase space variable.

Berry curvature characterizes entanglement entropy transitions.

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.