Berry phases, wormholes and factorization in AdS/CFT

Understand

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.