11 research outputs found
Dimensional reduction from entanglement in Minkowski space
Using a quantum field theoretic setting, we present evidence for dimensional
reduction of any sub-volume of Minkowksi space. First, we show that correlation
functions of a class of operators restricted to a sub-volume of D-dimensional
Minkowski space scale as its surface area. A simple example of such area
scaling is provided by the energy fluctuations of a free massless quantum field
in its vacuum state. This is reminiscent of area scaling of entanglement
entropy but applies to quantum expectation values in a pure state, rather than
to statistical averages over a mixed state. We then show, in a specific case,
that fluctuations in the bulk have a lower-dimensional representation in terms
of a boundary theory at high temperature.Comment: 9 pages, changes to presentation, some content corrections, version
published in JHE
Comments on No-Hair Theorems and Stabilty of Blackholes
In the light of recent blackhole solutions inspired by string theory, we
review some old statements on field theoretic hair on blackholes. We also
discuss some stability issues. In particular we argue that the two dimensional
string blackhole solution is semi-classically stable while the naked
singularity is unstable to tachyon fluctuations. Finally we comment on the
relation between the linear dilaton theory and the blackhole solution.Comment: 14 page
Thermodynamics and area in Minkowski space: Heat capacity of entanglement
Tracing over the degrees of freedom inside (or outside) a sub-volume V of
Minkowski space in a given quantum state |psi>, results in a statistical
ensemble described by a density matrix rho. This enables one to relate quantum
fluctuations in V when in the state |psi>, to statistical fluctuations in the
ensemble described by rho. These fluctuations scale linearly with the surface
area of V. If V is half of space, then rho is the density matrix of a canonical
ensemble in Rindler space. This enables us to `derive' area scaling of
thermodynamic quantities in Rindler space from area scaling of quantum
fluctuations in half of Minkowski space. When considering shapes other than
half of Minkowski space, even though area scaling persists, rho does not have
an interpretation as a density matrix of a canonical ensemble in a curved, or
geometrically non-trivial, background.Comment: 17 page
Effective Potentials for Light Moduli
We examine recent work on compactifications of string theory with fluxes,
where effective potentials for light moduli have been derived after integrating
out moduli that are assumed to be heavy at the classical level, and then adding
non-perturbative (NP) corrections to the superpotential. We find that this two
stage procedure is not valid and that the correct potential has additional
terms. Althought this does not affect the conclusion of Kachru et al (KKLT)
that the Kaehler moduli may be stabilized by NP effects, it can affect the
detailed physics. In particular it is possible to get metastable dS minima
without adding uplifting terms.Comment: Minor revisions, References added, Version to be published in PLB, 14
pages 3 figure
Moduli potentials in string compactifications with fluxes: mapping the Discretuum
We find de Sitter and flat space solutions with all moduli stabilized in four
dimensional supergravity theories derived from the heterotic and type II string
theories, and explain how all the previously known obstacles to finding such
solutions can be removed. Further, we argue that if the compact manifold allows
a large enough space of discrete topological choices then it is possible to
tune the parameters of the four dimensional supergravity such that a hierarchy
is created and the solutions lie in the outer region of moduli space in which
the compact volume is large in string units, the string coupling is weak, and
string perturbation theory is valid. We show that at least two light chiral
superfields are required for this scenario to work, however, one field is
sufficient to obtain a minimum with an acceptably small and negative
cosmological constant. We discuss cosmological issues of the scenario and the
possible role of anthropic considerations in choosing the vacuum of the theory.
We conclude that the most likely stable vacuua are in or near the central
region of moduli space where string perturbation theory is not strictly valid,
and that anthropic considerations cannot help much in choosing a vacuum.Comment: 34 pages, no figure
The Scales of Brane Nucleation Processes
The scales associated with Brown-Teitelboim-Bousso-Polchinski processes of
brane nucleation, which result in changes of the flux parameters and the number
of D-branes, are discussed in the context of type IIB models with all moduli
stabilized. It is argued that such processes are unlikely to be described by
effective field theory.Comment: some corrections made, conclusions unchanged, references added, 10
page
The Dynamics of Brane-World Cosmological Models
Brane-world cosmology is motivated by recent developments in string/M-theory
and offers a new perspective on the hierarchy problem. In the brane-world
scenario, our Universe is a four-dimensional subspace or {\em brane} embedded
in a higher-dimensional {\em bulk} spacetime. Ordinary matter fields are
confined to the brane while the gravitational field can also propagate in the
bulk, leading to modifications of Einstein's theory of general relativity at
high energies. In particular, the Randall-Sundrum-type models are
self-consistent and simple and allow for an investigation of the essential
non-linear gravitational dynamics. The governing field equations induced on the
brane differ from the general relativistic equations in that there are nonlocal
effects from the free gravitational field in the bulk, transmitted via the
projection of the bulk Weyl tensor, and the local quadratic energy-momentum
corrections, which are significant in the high-energy regime close to the
initial singularity. In this review we discuss the asymptotic dynamical
evolution of spatially homogeneous brane-world cosmological models containing
both a perfect fluid and a scalar field close to the initial singularity. Using
dynamical systems techniques it is found that, for models with a physically
relevant equation of state, an isotropic singularity is a past-attractor in all
orthogonal spatially homogeneous models (including Bianchi type IX models). In
addition, we describe the dynamics in a class of inhomogeneous brane-world
models, and show that these models also have an isotropic initial singularity.
These results provide support for the conjecture that typically the initial
cosmological singularity is isotropic in brane-world cosmology.Comment: Einstein Centennial Review Article: to appear in CJ