Berry phases, wormholes and factorization in AdS/CFT

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