167 research outputs found
Non-linear bigravity and cosmic acceleration
We explore the cosmological solutions of classes of non-linear bigravity
theories. These theories are defined by effective four-dimensional Lagrangians
describing the coupled dynamics of two metric tensors, and containing, in the
linearized limit, both a massless graviton and an ultralight one. We focus on
two paradigmatic cases: the case where the coupling between the two metrics is
given by a Pauli-Fierz-type mass potential, and the case where this coupling
derives from five-dimensional brane constructions. We find that cosmological
evolutions in bigravity theories can be described in terms of the dynamics of
two ``relativistic particles'', moving in a curved Lorenzian space, and
connected by some type of nonlinear ``spring''. Classes of bigravity
cosmological evolutions exhibit a ``locking'' mechanism under which the two
metrics ultimately stabilize in a bi-de-Sitter configuration, with relative
(constant) expansion rates. In the absence of matter, we find that a generic
feature of bigravity cosmologies is to exhibit a period of cosmic acceleration.
This leads us to propose bigravity as a source of a new type of dark energy
(``tensor quintessence''), exhibiting specific anisotropic features. Bigravity
could also have been the source of primordial inflation.Comment: 55 pages, 4 figures, references and comments added, final version
published in Phys. Rev.
Extended chiral algebras and the emergence of SU(2) quantum numbers in the Coulomb gas
We study a set of chiral symmetries contained in degenerate operators beyond
the `minimal' sector of the c(p,q) models. For the operators
h_{(2j+2)q-1,1}=h_{1,(2j+2)p-1} at conformal weight [ (j+1)p-1 ][ (j+1)q -1 ],
for every 2j \in N, we find 2j+1 chiral operators which have quantum numbers of
a spin j representation of SU(2). We give a free-field construction of these
operators which makes this structure explicit and allows their OPEs to be
calculated directly without any use of screening charges. The first non-trivial
chiral field in this series, at j=1/2, is a fermionic or para-fermionic
doublet. The three chiral bosonic fields, at j=1, generate a closed W-algebra
and we calculate the vacuum character of these triplet models.Comment: 23 pages Late
Effective Lagrangians and Universality Classes of Nonlinear Bigravity
We discuss the fully non-linear formulation of multigravity. The concept of
universality classes of effective Lagrangians describing bigravity, which is
the simplest form of multigravity, is introduced. We show that non-linear
multigravity theories can naturally arise in several different physical
contexts: brane configurations, certain Kaluza-Klein reductions and some
non-commutative geometry models. The formal and phenomenological aspects of
multigravity (including the problems linked to the linearized theory of massive
gravitons) are briefly discussed.Comment: 41 pages, 4 Figures, final version to be published in Phys.Rev.
Extended chiral algebras in the SU(2)_0 WZNW model
We investigate the W-algebras generated by the integer dimension chiral
primary operators of the SU(2)_0 WZNW model. These have a form almost identical
to that found in the c=-2 model but have, in addition, an extended Kac-Moody
structure. Moreover on Hamiltonian reduction these SU(2)_0 W-algebras exactly
reduce to those found in c=-2. We explicitly find the free field
representations for the chiral j=2 and j=3 operators which have respectively a
fermionic doublet and bosonic triplet nature. The correlation functions of
these operators accounts for the rational solutions of the
Knizhnik-Zamolodchikov equation that we find. We explicitly compute the full
algebra of the j=2 operators and find that the associativity of the algebra is
only guaranteed if certain null vectors decouple from the theory. We conjecture
that these algebras may produce a quasi-rational conformal field theory.Comment: 18 pages LATEX. Minor corrections. Full j=2 algebra adde
Area Law and Continuum Limit in "Induced QCD"
We investigate a class of operators with non-vanishing averages in a
D-dimensional matrix model recently proposed by Kazakov and Migdal. Among the
operators considered are ``filled Wilson loops" which are the most reasonable
counterparts of Wilson loops in the conventional Wilson formulation of lattice
QCD. The averages of interest are represented as partition functions of certain
2-dimensional statistical systems with nearest neighbor interactions. The
``string tension" , which is the exponent in the area law for the
``filled Wilson loop" is equal to the free energy density of the corresponding
statistical system. The continuum limit of the Kazakov--Migdal model
corresponds to the critical point of this statistical system. We argue that in
the large limit this critical point occurs at zero temperature. In this
case we express in terms of the distribution density of eigenvalues
of the matrix-valued master field. We show that the properties of the continuum
limit and the description of how this limit is approached is very unusual and
differs drastically from what occurs in both the Wilson theory () and in the ``adjoint'' theory (). Instead, the continuum limit of the model appears to be
intriguingly similar to a string theory.Comment: 38 page
Cosmic Strings in a Braneworld Theory with Metastable Gravitons
If the graviton possesses an arbitrarily small (but nonvanishing) mass,
perturbation theory implies that cosmic strings have a nonzero Newtonian
potential. Nevertheless in Einstein gravity, where the graviton is strictly
massless, the Newtonian potential of a cosmic string vanishes. This discrepancy
is an example of the van Dam--Veltman--Zakharov (VDVZ) discontinuity. We
present a solution for the metric around a cosmic string in a braneworld theory
with a graviton metastable on the brane. This theory possesses those features
that yield a VDVZ discontinuity in massive gravity, but nevertheless is
generally covariant and classically self-consistent. Although the cosmic string
in this theory supports a nontrivial Newtonian potential far from the source,
one can recover the Einstein solution in a region near the cosmic string. That
latter region grows as the graviton's effective linewidth vanishes (analogous
to a vanishing graviton mass), suggesting the lack of a VDVZ discontinuity in
this theory. Moreover, the presence of scale dependent structure in the metric
may have consequences for the search for cosmic strings through gravitational
lensing techniques.Comment: 18 pages, 2 figures, revtex. Improved discussion of interpolating
solution. To be published in Phys. Rev.
Conformal Orbifold Partition Functions from Topologically Massive Gauge Theory
We continue the development of the topological membrane approach to open and
unoriented string theories. We study orbifolds of topologically massive gauge
theory defined on the geometry , where is a generic
compact Riemann surface. The orbifold operations are constructed by gauging the
discrete symmetries of the bulk three-dimensional field theory. Multi-loop
bosonic string vacuum amplitudes are thereby computed as bulk correlation
functions of the gauge theory. It is shown that the three-dimensional
correlators naturally reproduce twisted and untwisted sectors in the case of
closed worldsheet orbifolds, and Neumann and Dirichlet boundary conditions in
the case of open ones. The bulk wavefunctions are used to explicitly construct
the characters of the underlying extended Kac-Moody group for arbitrary genus.
The correlators for both the original theory and its orbifolds give the
expected modular invariant statistical sums over the characters.Comment: 47 pages LaTeX, 3 figures, uses amsfonts and epsfig; v2: Typos
corrected, reference added, clarifying comments on modular invariance
inserted; v3: Further comments on modular invariance added; to be published
in JHE
Extended multiplet structure in Logarithmic Conformal Field Theories
We use the process of quantum hamiltonian reduction of SU(2)_k, at rational
level k, to study explicitly the correlators of the h_{1,s} fields in the
c_{p,q} models. We find from direct calculation of the correlators that we have
the possibility of extra, chiral and non-chiral, multiplet structure in the
h_{1,s} operators beyond the `minimal' sector. At the level of the vacuum null
vector h_{1,2p-1}=(p-1)(q-1) we find that there can be two extra non-chiral
fermionic fields. The extra indicial structure present here permeates
throughout the entire theory. In particular we find we have a chiral triplet of
fields at h_{1,4p-1}=(2p-1)(2q-1). We conjecture that this triplet algebra may
produce a rational extended c_{p,q} model. We also find a doublet of fields at
h_{1,3p-1}=(\f{3p}{2}-1)(\f{3q}{2}-1). These are chiral fermionic operators if
p and q are not both odd and otherwise parafermionic.Comment: 24 pages LATEX. Minor corrections and extra reference
Conformal Dimensions from Topologically Massive Quantum Field Theory
We discuss the evaluation of observables in two-dimensional conformal field
theory using the topological membrane description. We show that the spectrum of
anomalous dimensions can be obtained perturbatively from the topologically
massive quantum field theories by computing radiative corrections to
Aharonov-Bohm scattering amplitudes for dynamical charged matter fields. The
one-loop corrections in the case of topologically massive Yang-Mills theory are
shown to coincide with the scaling dimensions of the induced ordinary and
supersymmetric WZNW models. We examine the effects of the dressing of a
topologically massive gauge theory by topologically massive gravity and show
that the one-loop contributions to the Aharonov-Bohm amplitudes coincide with
the leading orders of the KPZ scaling relations for two-dimensional quantum
gravity. Some general features of the description of conformal field theories
via perturbative techniques in the three-dimensional approach are also
discussed.Comment: 48 pages Latex; Uses macro package FEYNMAN.te
Multigravity in six dimensions: Generating bounces with flat positive tension branes
We present a generalization of the five dimensional multigravity models to
six dimensions. The key characteristic of these constructions is that that we
obtain solutions which do not have any negative tension branes while at the
same time the branes are kept flat. This is due to the fact that in six
dimensions the internal space is not trivial and its curvature allows bounce
configurations with the above feature. These constructions give for the first
time a theoretically and phenomenologically viable realization of multigravity.Comment: 27 pages, 13 figures, typos correcte
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