bibkey: jlms2016relativeentropy authors: Daniel L. Jafferis, Aitor Lewkowycz, Juan Maldacena, and S. Josephine Suh year: 2016 title: Relative entropy equals bulk relative entropy doi: 10.1007/JHEP06(2016)004 claim: Nearby-state bulk/boundary relative entropy and modular-flow relation in a holographic setting at leading bulk gravitational order. strata_touched: [] license: citation-only triage: anchor

Holographic relative entropy

JLMS study the gravitational dual of a boundary subregion modular Hamiltonian. Their abstract argues for equality of relative entropy of nearby states with bulk relative entropy to leading order in the bulk gravitational coupling, and relates boundary modular flow to bulk modular flow in the entanglement wedge. The claim presupposes a chosen holographic dual and does not follow from a VOA or a formal Mobius inversion alone.

The holographic interpretation of appendix 2143 therefore concerns additional data: a concrete dual model and dictionary, a chosen boundary region and its bulk entanglement wedge, and compatible nearby semiclassical states, region algebras, and modular flows. A semiclassical code subspace is additional encoding data, not a consequence of that appendix. The abstract’s leading-order equality is not an exact relative-entropy identity for arbitrary states, nor a universal AdS dual for arbitrary VOAs. The broader duality proposal has its own scope in the Maldacena note.

Verified locator

• Manuscript and abstract: https://arxiv.org/abs/1512.06431
• Published DOI: https://doi.org/10.1007/JHEP06(2016)004

The abstract and bibliographic identity were checked; the full paper was not inspected.