192 research outputs found
An Uneventful Horizon in Two Dimensions
We investigate the possibility of firewalls in the Einstein-dilaton gravity
model of CGHS. We use the results of the numerical simulation carried out by
Ashtekar et al. to demonstrate that firewalls are absent and the horizon is
drama free. We show that the lack of a firewall is consistent because the model
does not satisfy one of the postulates of black hole complementarity. In
particular, we show that the Hawking radiation is not pure, and is completely
entangled with a long-lived remnant beyond the last ray.Comment: 28 pages, 4 figure
Holographic Reconstruction of General Bulk Surfaces
We propose a reconstruction of general bulk surfaces in any dimension in
terms of the differential entropy in the boundary field theory. In particular,
we extend the proof of Headrick et al. to calculate the area of a general class
of surfaces, which have a 1-parameter foliation over a closed manifold. The
area can be written in terms of extremal surfaces whose boundaries lie on
ring-like regions in the field theory. We discuss when this construction has a
description in terms of spatial entanglement entropy and suggest lessons for a
more complete and covariant approach.Comment: 21 pages, 10 figures; v2: minor clarifications, references added,
published versio
Spinning Geodesic Witten Diagrams
We present an expression for the four-point conformal blocks of symmetric
traceless operators of arbitrary spin as an integral over a pair of geodesics
in Anti-de Sitter space, generalizing the geodesic Witten diagram formalism of
Hijano et al [arXiv:1508.00501] to arbitrary spin. As an intermediate step in
the derivation, we identify a convenient basis of bulk three-point interaction
vertices which give rise to all possible boundary three point structures. We
highlight a direct connection between the representation of the conformal block
as a geodesic Witten diagram and the shadow operator formalism.Comment: 28+6 pages, 8 figure
Integral Geometry and Holography
We present a mathematical framework which underlies the connection between
information theory and the bulk spacetime in the AdS/CFT
correspondence. A key concept is kinematic space: an auxiliary Lorentzian
geometry whose metric is defined in terms of conditional mutual informations
and which organizes the entanglement pattern of a CFT state. When the field
theory has a holographic dual obeying the Ryu-Takayanagi proposal, kinematic
space has a direct geometric meaning: it is the space of bulk geodesics studied
in integral geometry. Lengths of bulk curves are computed by kinematic volumes,
giving a precise entropic interpretation of the length of any bulk curve. We
explain how basic geometric concepts -- points, distances and angles -- are
reflected in kinematic space, allowing one to reconstruct a large class of
spatial bulk geometries from boundary entanglement entropies. In this way,
kinematic space translates between information theoretic and geometric
descriptions of a CFT state. As an example, we discuss in detail the static
slice of AdS whose kinematic space is two-dimensional de Sitter space.Comment: 23 pages + appendices, including 23 figures and an exercise sheet
with solutions; a Mathematica visualization too
Bulk and Transhorizon Measurements in AdS/CFT
We discuss the construction of bulk operators in asymptotically AdS
spacetimes, including the interiors of AdS black holes. We use this to address
the question "If Schrodinger's cat were behind the horizon of an AdS black
hole, could we determine its state by a measurement in the dual CFT?"Comment: 32 pages, 5 figures. v2: Author added, appendix on spacelike Green's
function added, discussion of non-dependence on boundary Hamiltonian expande
Modular Berry Connection
The Berry connection describes transformations induced by adiabatically
varying Hamiltonians. We study how zero modes of the modular Hamiltonian are
affected by varying the region that supplies the modular Hamiltonian. In the
vacuum of a 2d CFT, global conformal symmetry singles out a unique modular
Berry connection, which we compute directly and in the dual AdS picture. In
certain cases, Wilson loops of the modular Berry connection compute lengths of
curves in AdS, reproducing the differential entropy formula. Modular Berry
transformations can be measured by bulk observers moving with varying
accelerations.Comment: 5 pages, 2 figures. Some clarifications adde
Black Holes: Complementarity or Firewalls?
We argue that the following three statements cannot all be true: (i) Hawking
radiation is in a pure state, (ii) the information carried by the radiation is
emitted from the region near the horizon, with low energy effective field
theory valid beyond some microscopic distance from the horizon, and (iii) the
infalling observer encounters nothing unusual at the horizon. Perhaps the most
conservative resolution is that the infalling observer burns up at the horizon.
Alternatives would seem to require novel dynamics that nevertheless cause
notable violations of semiclassical physics at macroscopic distances from the
horizon.Comment: 22 pages, 1 figure. v2: We have not changed our minds. Various
arguments are expanded and sharpened. v3: Relation to previous work
clarified. v4: Additional reference to earlier wor
Tensor networks from kinematic space
We point out that the MERA network for the ground state of a 1+1-dimensional
conformal field theory has the same structural features as kinematic
space---the geometry of CFT intervals. In holographic theories kinematic space
becomes identified with the space of bulk geodesics studied in integral
geometry. We argue that in these settings MERA is best viewed as a
discretization of the space of bulk geodesics rather than of the bulk geometry
itself. As a test of this kinematic proposal, we compare the MERA
representation of the thermofield-double state with the space of geodesics in
the two-sided BTZ geometry, obtaining a detailed agreement which includes the
entwinement sector. We discuss how the kinematic proposal can be extended to
excited states by generalizing MERA to a broader class of compression networks.Comment: 35 pages, 17 figure
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