Berry phases, wormholes and factorization in AdS/CFT
- URL: http://arxiv.org/abs/2202.11717v2
- Date: Fri, 4 Mar 2022 16:03:07 GMT
- Title: Berry phases, wormholes and factorization in AdS/CFT
- Authors: Souvik Banerjee, Moritz Dorband, Johanna Erdmenger, Ren\'e Meyer and
Anna-Lena Weigel
- Abstract summary: 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.
We classify Berry phases in holographic CFTs based on the type of dual bulk diffeomorphism involved.
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.
- Score: 0.0
- License: http://creativecommons.org/licenses/by-sa/4.0/
- 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.
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