40 research outputs found
Time Evolution after Double Trace Deformation
In this paper, we consider double trace deformation to single CFT, and
study time evolution after the deformation. The double trace deformation we
consider is nonlocal: composed of two local operators placed at separate
points. We study two types of local operators: one is usual local operator in
CFT, and the other is HKLL bulk local operator, which is still operator in CFT
but has properties as bulk local operator. We compute null energy and averaged
null energy in the bulk in both types of deformations. We confirmed that, with
the suitable choice of couplings, averaged null energies are negative. This
implies causal structure is modified in the bulk, from classical background. We
then calculate time evolution of entanglement entropy and entanglement Renyi
entropy after double trace deformation. We find both quantities are found to
show peculiar shockwave-like time evolution.Comment: 16 pages, 12 figures, references added, typos correcte
Butterflies from Information Metric
We study time evolution of distance between thermal states excited by local
operators, with different external couplings. We find that growth of the
distance implies growth of commutators of operators, signifying the local
excitations are scrambled. We confirm this growth of distance by holographic
computation, by evaluating volume of codimension 1 extremal volume surface. We
find that the distance increases exponentially as .
Our result implies that, in chaotic system, trajectories of excited thermal
states exhibit high sensitivity to perturbation to the Hamiltonian, and the
distance between them will be significant at the scrambling time. We also
confirm the decay of two point function of holographic Wilson loops on
thermofield double state.Comment: 10 pages, 3 figures, reference added, minor modification
Surface/State Correspondence as a Generalized Holography
We propose a new duality relation between codimension two space-like surfaces
in gravitational theories and quantum states in dual Hilbert spaces. This
surface/state correspondence largely generalizes the idea of holography such
that we do not need to rely on any existence of boundaries in gravitational
spacetimes. The present idea is motivated by the recent interpretation of
AdS/CFT in terms of the tensor networks so called MERA. Moreover, we study this
correspondence from the viewpoint of entanglement entropy and information
metric. The Cramer-Rao bound in quantum estimation theory implies that the
quantum fluctuations of radial coordinate of the AdS is highly suppressed in
the large N limit.Comment: 28 pages, 4 figures, Late
Causal Evolutions of Bulk Local Excitations from CFT
Bulk localized excited states in an AdS spacetime can be constructed from
Ishibashi states with respect to the global conformal symmetry in the dual CFT.
We study boundary two point functions of primary operators in the presence of
bulk localized excitations in two dimensional CFTs. From two point functions in
holographic CFTs, we observe causal propagations of radiations when the mass of
dual bulk scalar field is close to the BF bound. This behavior for holographic
CFTs is consistent with the locality and causality in classical gravity duals.
We also show that this cannot be seen in free fermion CFTs. Moreover, we find
that the short distance behavior of two point functions is universal and obeys
the relation which generalizes the first law of entanglement entropy.Comment: 23pages, Late
Holographic Entanglement of Purification from Conformal Field Theories
We explore a conformal field theoretic interpretation of the holographic
entanglement of purification, which is defined as the minimal area of
entanglement wedge cross section. We argue that in AdS3/CFT2, the holographic
entanglement of purification agrees with the entanglement entropy for a
purified state, obtained from a special Weyl transformation, called
path-integral optimizations. By definition, this special purified state has the
minimal path-integral complexity. We confirm this claim in several examples.Comment: 7 pages, Revtex, 5 figure
Holographic BCFT with a Defect on the End-of-the-World Brane
In this paper, we propose a new gravity dual for a d BCFT with two
conformal boundaries by introducing a defect that connects the two
End-of-the-World branes. We demonstrate that the BCFT dual to this bulk model
exhibits a richer lowest spectrum. The corresponding lowest energy eigenvalue
can continuously interpolate between and where
is the distance between the boundaries. This range was inaccessible
to the conventional AdS/BCFT model with distinct boundary conditions. We
compute the holographic entanglement entropy and find that it exhibits three
different phases, one of which breaks the time reflection symmetry. We also
construct a wormhole saddle, analogous to a d replica wormhole, which
connects different boundaries through the AdS bulk. This saddle is present only
if the BCFT is non-unitary and is always subdominant compared to the
disconnected saddle.Comment: 23+5 pages, 6 figure
Fluctuation in the Fidelity of Information Recovery from Hawking Radiation
The interior of a pure-state black hole is known to be reconstructed from the
Petz map by collecting a sufficiently large amount of the emitted Hawking
radiation. This was established based on the Euclidean replica wormhole, which
comes from an ensemble averaging over gravitational theories. On the other
hand, this means that the Page curve and the interior reconstruction are both
ensemble averages; thus, there is a possibility of large errors. In the
previous study [Bousso, Miyaji (2023)], it was shown that the entropy of the
Hawking radiation has fluctuation of order , thus is
typical in the ensemble. In the present article, we show that the fluctuations
of the relative entropy difference in the encoding map and the entanglement
fidelity of the Petz map are both suppressed by compared
to the signals, establishing the typicality in the ensemble. In addition, we
also compute the entanglement loss of the encoding map.Comment: 17 pages, 3 figures, v2: typos correcte
Fluctuations in the Entropy of Hawking Radiation
We use the gravitational path integral (GPI) to compute the fluctuations of
the Hawking radiation entropy around the Page curve, in a two-dimensional model
introduced by Penington \emph{et al}. Before the Page time, we find that
, where is the black hole entropy. This result
agrees with the Haar-averaged entropy fluctuations of a bipartite system, which
we also compute at leading order. After the Page time, we find that , up to a prefactor that depends logarithmically on the width of
the microcanonical energy window. This is not symmetric under exchange of
subsystem sizes and so does not agree with the Haar average for a subsystem of
fixed Hilbert space dimension. The discrepancy can be attributed to the fact
that the black hole Hilbert space dimension is not fixed by the state
preparation: even in a microcanonical ensemble with a top-hat smearing
function, the GPI yields an additive fluctuation in the number of black hole
states. This result, and the fact that the Page curve computed by the GPI is
smooth, all point towards an ensemble interpretation of the GPI.Comment: 18 pages, 3 figures, v2: incorporates improved results on
fluctuations in bipartite systems [31
Anti-de Sitter Space from Optimization of Path Integrals in Conformal Field Theories
We introduce a new optimization procedure for Euclidean path integrals which
compute wave functionals in conformal field theories (CFTs). We optimize the
background metric in the space on which the path integration is performed.
Equivalently this is interpreted as a position-dependent UV cutoff. For
two-dimensional CFT vacua, we find the optimized metric is given by that of a
hyperbolic space and we interpret this as a continuous limit of the conjectured
relation between tensor networks and Anti--de Sitter (AdS)/conformal field
theory (CFT) correspondence. We confirm our procedure for excited states, the
thermofield double state, the Sachdev-Ye-Kitaev model and discuss its extension
to higher-dimensional CFTs. We also show that when applied to reduced density
matrices, it reproduces entanglement wedges and holographic entanglement
entropy. We suggest that our optimization prescription is analogous to the
estimation of computational complexity.Comment: 7 pages, Revtex, 2 figures, Version 2 : The version published in PRL,
title expanded and typos correcte