TY - JOUR

T1 - More of the bulk from extremal area variations

AU - Bao, Ning

AU - Cao, ChunJun

AU - Fischetti, Sebastian

AU - Pollack, Jason

AU - Zhong, Yibo

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

KW - AdS

KW - CFT

KW - bulk reconstruction

KW - holography

KW - inverse boundary value problems

KW - entanglement entropy

KW - SPACE-TIME

KW - PERTURBATIONS

KW - MEMBRANES

KW - SYSTEMS

KW - STRINGS

U2 - 10.1088/1361-6382/abcfd0

DO - 10.1088/1361-6382/abcfd0

M3 - Journal article

VL - 38

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

SN - 0264-9381

IS - 4

M1 - 047001

ER -