Pure states for subregions in gravity and their entanglement entropy

Abstract:It is proposed that spatial subregions in quantum gravity can be assigned pure states, rather than mixed reduced density matrices. The state is prepared by a partially frozen gravitational path integral, in which a spacetime subregion containing the spatial subregion is fixed while the field configurations and ambient geometry are summed over. In the semiclassical regime, we further propose a holographic prescription for the entanglement entropy of bipartitions of this state, with a frozen-region analogue of the homology constraint. The prescription satisfies nontrivial self-consistency conditions, including strong subadditivity, complementarity, and entanglement wedge nesting, and reproduces several known entropy formulas in holography and gravity as special cases. The construction suggests an observer-dependent entanglement wedge labeled by the frozen subregion.

arXiv:2606.03977 [hep-th]

(or arXiv:2606.03977v1 [hep-th] for this version)

https://doi.org/10.48550/arXiv.2606.03977 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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