11 research outputs found
Holographic bulk reconstruction beyond (super)gravity
We outline a holographic recipe to reconstruct corrections to AdS
(quantum) gravity from an underlying CFT in the strictly planar limit
(). Assuming that the boundary CFT can be solved in
principle to all orders of the 't Hooft coupling , for scalar primary
operators, the expansion of the conformal dimensions can be
mapped to higher curvature corrections of the dual bulk scalar field action.
Furthermore, for the metric pertubations in the bulk, the AdS/CFT
operator-field isomorphism forces these corrections to be of the Lovelock type.
We demonstrate this by reconstructing the coefficient of the leading Lovelock
correction, aka the Gauss-Bonnet term in a bulk AdS gravity action using the
expression of stress-tensor two-point function up to sub-leading order in
.Comment: 19 pages, typos corrected, published version (journal version title
is different
On Some Universal Features of the Holographic Quantum Complexity of Bulk Singularities
We perform a comparative study of the time dependence of the holographic
quantum complexity of some space like singular bulk gravitational backgrounds.
This is done by considering the two available notions of complexity, one that
relates it to the maximal spatial volume and the other that relates it to the
classical action of the Wheeler-de Witt patch. We calculate and compare the
leading and the next to leading terms and find some universal features. The
complexity decreases towards the singularity for both definitions, for all
types of singularities studied. In addition the leading terms have the same
quantitative behavior for both definitions in restricted number of cases and
the behaviour itself is different for different singular backgrounds. The
quantitative details of the next to leading terms, such as their specific form
of time dependence, are found not to be universal. They vary between the
different cases and between the different bulk definitions of complexity. We
also address some technical points inherent to the calculation.Comment: 24 pages, 6 figures. v2: minor correction
Bulk metric reconstruction from boundary entanglement
Most of the literature in the \emph{bulk reconstruction program} in
holography focuses on recovering local bulk operators propagating on a
quasilocal bulk geometry and the knowledge of the bulk geometry is always
assumed or guessed. The fundamental problem of the bulk reconstruction program,
which is \emph{recovering the bulk background geometry (metric)} from the
boundary CFT state is still outstanding. In this work, we formulate a recipe to
extract the bulk metric itself from the boundary state, specifically, the
modular Hamiltonian information of spherical subregions in the boundary. Our
recipe exploits the recent construction of Kabat and Lifschytz
\cite{Kabat:2017mun} to first compute the bulk two point function of scalar
fields directly in the CFT without knowledge of the bulk metric or the
equations of motion, and then to take a large scaling dimension limit (WKB) to
extract the geodesic distance between two close points in the bulk i.e. the
metric. As a proof of principle, we consider three dimensional bulk and
selected CFT states such as the vacuum and the thermofield double states. We
show that they indeed reproduce the pure AdS and the regions outside the
Rindler wedge and the BTZ black hole \emph{up to a rigid conformal factor}.
Since our approach does not rely on symmetry properties of the CFT state, it
can be applied to reconstruct asymptotically AdS geometries dual to arbitrary
general CFT states provided the modular Hamiltonian is available. We discuss
several obvious extensions to the case of higher spacetime dimensions as well
as some future applications, in particular, for constructing metric beyond the
causal wedge of a boundary region. In the process, we also extend the
construction of \cite{Kabat:2017mun} to incorporate the first order
perturbative locality for AdS scalars.Comment: 16+4 pages, 3 figures; v2: some clarifications and references added;
v3: more clarifications added. Published versio
CFT reconstruction of local bulk operators in half-Minkowski space
We construct a holographic map that reconstructs massless fields (scalars,
Maxwell field \& Fierz-Pauli field) in half-Minkowski spacetime in
dimensions terms of smeared primary operators in a large factorizable CFT
in spacetime dimensions. This map is based on a Weyl
(rescaling) transformation from the Poincar\'e wedge of AdS to the Minkowski
half-space; and on the HKLL smearing function, which reconstructs local bulk
operators in the Poincar\'e AdS in terms of smeared operators on the conformal
boundary of the Poincar\'e wedge. The massless scalar field is reconstructed up
to the level of two-point functions, while the Maxwell field and massless
spin-2 fields are reconstructed at the level of the one-point function. We also
discuss potential ways the map can be generalized to higher dimensions, and to
the full Minkowski space.Comment: Updated bibliography, Updated discussion section, 20 pages, 2 figure
Holographic Complexity of LST and Single Trace
In this work, we continue our study of string theory in the background that
interpolates between in the IR to flat spacetime with a linear dilaton
in the UV. The boundary dual theory interpolates between a CFT in the IR to
a certain two-dimensional Little String Theory (LST) in the UV. In particular,
we study \emph{computational complexity} of such a theory through the lens of
holography and investigate the signature of non-locality in the short distance
behavior of complexity. When the cutoff UV scale is much smaller than the
non-locality (Hagedorn) scale, we find exotic quadratic and logarithmic
divergences (for both volume and action complexity) which are not expected in a
local quantum field theory. We also generalize our computation to include the
effects of finite temperature. Up to second order in finite temperature
correction, we do not any find newer exotic UV-divergences compared to the zero
temperature case.Comment: Appendix A and few references added. 28 pages+1 appendi
Holographic description of black holes and cosmic inflation in asymptotically anti de Sitter backgrounds
Abstract not available
Complexity of warped conformal field theory
Warped conformal field theories in two dimensions are exotic nonlocal, Lorentz violating field theories characterized by Virasoro–Kac–Moody symmetries and have attracted a lot of attention as candidate boundary duals to warped AdS spacetimes, thereby expanding the scope of holography beyond asymptotically AdS spacetimes. Here we investigate WCFT s using circuit complexity as a tool. First we compute the holographic volume complexity (CV) which displays a linear UV divergence structure, more akin to that of a local CFT and has a very complicated dependence on the Virasoro central charge c and the U(1) Kac–Moody level parameter k. Next we consider circuit complexity based on Virasoro–Kac–Moody symmetry gates where the complexity functional is the geometric (group) action on coadjoint orbits of the Virasoro–Kac–Moody group. We consider a special solution to extremization equations for which complexity scales linearly with “time”. In the semiclassical limit (large c, k, while c/k remains finite and small) both the holographic volume complexity and circuit complexity scales with k