More of the bulk from extremal area variations
Abstract
It was shown recently in (Bao N et al 2019 Class. Quantum Grav. 36 185002), building on work of Alexakis, Balehowksy, and Nachman (Alexakis S et al 2017 arXiv:1711.09379), that the geometry of (some portion of) a manifold with boundary is uniquely fixed by the areas of a foliation of two-dimensional disk-shaped surfaces anchored to the boundary. In the context of AdS/CFT, this implies that (a portion of) a four-dimensional bulk geometry can be fixed uniquely from the entanglement entropies of disk-shaped boundary regions, subject to several constraints. In this note, we loosen some of these constraints, in particular allowing for the bulk foliation of extremal surfaces to be local and removing the constraint of disk topology; these generalizations ensure uniqueness of more of the deep bulk geometry by allowing for e.g. surfaces anchored on disconnected asymptotic boundaries, or HRT surfaces past a phase transition. We also explore in more depth the generality of the local foliation requirement, showing that even in a highly dynamical geometry like AdS-Vaidya it is satisfied.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Dec 24, 2020
- Source ID
- 10.1088/1361-6382/abcfd0
Entities
People
- Chunjun Cao
- Jason Pollack
- Ning Bao
- Sebastian Fischetti
- Yibo Zhong
Organizations
- Division of Physics
- National Institute of Standards and Technology
- Natural Sciences and Engineering Research Council
- Simons Foundation
- United States Department of Defense
- United States Department of Energy