2,789 research outputs found
Holographic Construction of Excited CFT States
We present a systematic construction of bulk solutions that are dual to CFT
excited states. The bulk solution is constructed perturbatively in bulk fields.
The linearised solution is universal and depends only on the conformal
dimension of the primary operator that is associated with the state via the
operator-state correspondence, while higher order terms depend on detailed
properties of the operator, such as its OPE with itself and generally involve
many bulk fields. We illustrate the discussion with the holographic
construction of the universal part of the solution for states of two
dimensional CFTs, either on or on . We compute the
1-point function both in the CFT and in the bulk, finding exact agreement. We
comment on the relation with other reconstruction approaches.Comment: 26 pages, 4 figures, v2: comments adde
Thermal diffractive corrections to Casimir energies
We study the interplay of thermal and diffractive effects in Casimir
energies. We consider plates with edges, oriented either parallel or
perpendicular to each other, as well as a single plate with a slit. We compute
the Casimir energy at finite temperature using a formalism in which the
diffractive effects are encoded in a lower dimensional non-local field theory
that lives in the gap between the plates. The formalism allows for a clean
separation between direct or geometric effects and diffractive effects, and
makes an analytic derivation of the temperature dependence of the free energy
possible. At low temperatures, with Dirichlet boundary conditions on the
plates, we find that diffractive effects make a correction to the free energy
which scales as T^6 for perpendicular plates, as T^4 for slits, and as T^4 log
T for parallel plates.Comment: 31 pages, 7 figures, LaTeX. v2: minor typos fixed, version to appear
in PR
Holographic representation of local bulk operators
The Lorentzian AdS/CFT correspondence implies a map between local operators
in supergravity and non-local operators in the CFT. By explicit computation we
construct CFT operators which are dual to local bulk fields in the
semiclassical limit. The computation is done for general dimension in global,
Poincare and Rindler coordinates. We find that the CFT operators can be taken
to have compact support in a region of the complexified boundary whose size is
set by the bulk radial position. We show that at finite N the number of
independent commuting operators localized within a bulk volume saturates the
holographic bound.Comment: 36 pages, LaTeX, 4 eps figure
A Comment on Zero-brane Quantum Mechanics
We consider low energy, non-relativistic scattering of two Dirichlet
zero-branes as an exercise in quantum mechanics. For weak string coupling and
sufficiently small velocity, the dynamics is governed by an effective U(2)
gauge theory in 0+1 dimensions. At low energies, D-brane scattering can
reliably probe distances much shorter than the string scale. The only length
scale in the quantum mechanics problem is the eleven dimensional Planck length.
This provides evidence for the role of scales shorter than the string length in
the weakly coupled dynamics of type IIA strings.Comment: 9 pages, harvmac, improved treatment of 2+1 proble
Constructing local bulk observables in interacting AdS/CFT
Local operators in the bulk of AdS can be represented as smeared operators in
the dual CFT. We show how to construct these bulk observables by requiring that
the bulk operators commute at spacelike separation. This extends our previous
work by taking interactions into account. Large-N factorization plays a key
role in the construction. We show diagrammatically how this procedure is
related to bulk Feynman diagrams.Comment: 41 pages, LaTeX. v2: reference correcte
Point-Like Graviton Scattering in Plane-Wave Matrix Model
In a plane-wave matrix model we discuss a two-body scattering of gravitons in
the SO(3) symmetric space. In this case the graviton solutions are point-like
in contrast to the scattering in the SO(6) symmetric space where spherical
membranes are interpreted as gravitons. We concentrate on a configuration in
the 1-2 plane where a graviton rotates with a constant radius and the other one
elliptically rotates. Then the one-loop effective action is computed by using
the background field method. As the result, we obtain the 1/r^7-type
interaction potential, which strongly suggests that the scattering in the
matrix model would be closely related to that in the light-front
eleven-dimensional supergravity.Comment: 17 pages, 1 figure, LaTeX, v2) references adde
A Comment on the Geometric Entropy and Conical Space
It has been recently pointed out that a definition of the geometric entropy
using the partition function in a conical space does not in general lead to a
positive definite quantity. For a scalar field model with a non-minimal
coupling we clarify the origin of the anomalous behavior from the viewpoint of
the canonical formulation.Comment: No Figures. To appear in Classical and Quantum Gravit
Local bulk operators in AdS/CFT: a boundary view of horizons and locality
We develop the representation of local bulk fields in AdS by non-local
operators on the boundary, working in the semiclassical limit and using AdS_2
as our main example. In global coordinates we show that the boundary operator
has support only at points which are spacelike separated from the bulk point.
We construct boundary operators that represent local bulk operators inserted
behind the horizon of the Poincare patch and inside the Rindler horizon of a
two dimensional black hole. We show that these operators respect bulk locality
and comment on the generalization of our construction to higher dimensional AdS
black holes.Comment: 28 pages, 4 figures, late
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