70 research outputs found
Higher spin fields from indefinite Kac-Moody algebras
The emergence of higher spin fields in the Kac-Moody theoretic approach to
M-theory is studied. This is based on work done by Schnakenburg, West and the
second author. We then study the relation of higher spin fields in this
approach to other results in different constructions of higher spin field
dynamics. Of particular interest is the construction of space-time in the
present set-up and we comment on the various existing proposals.Comment: 1+18 pages. Based on a talk presented by A. Kleinschmidt at the First
Solvay Workshop on Higher-Spin Gauge Theories held in Brussels on May 12-14,
200
Dualities and signatures of G++ invariant theories
The G++ content of the formulation of gravity and M-theories as very-extended
Kac-Moody invariant theories is further analysed. The different exotic phases
of all the G_B++ theories, which admit exact solutions describing intersecting
branes smeared in all directions but one, are derived. This is achieved by
analysing for all G++ the signatures which are related to the conventional one
(1,D-1) by `dualities' generated by the Weyl reflections.Comment: 26 pages, 3 figure
Kac-Moody Algebras in M-theory
In this thesis, we consider several aspects of over-extended and
very-extended Kac-Moody algebras in relation with theories of gravity coupled
to matter. In the first part, we focus on the occurrence of KM algebras in the
cosmological billiards. We analyse the billiards in the simplified situation of
spatially homogeneous cosmologies. The most generic cases lead to the same
algebras as those met in the general inhomogeneous case, but also sub-algebras
of the "generic" ones appear. Next, we consider particular gravitational
theories which, upon toroidal compactification to D=3 space-time dimensions,
reduce to a theory of gravity coupled to a symmetric space non-linear
sigma-model. We show that the billiard analysis gives direct information on
possible dimensional oxidations (or on their obstructions) and field content of
the oxidation endpoint. We also consider all hyperbolic Kac-Moody algebras and
completely answer the question of whether or not a specific theory exists
admitting a billiard characterised by the given hyperbolic algebra. In the
second part, we turn to the set up of such gravity-matter theories through the
building of an action explicitly invariant under a Kac-Moody group. As a first
step to include fermions, we check the compatibility of the presence of a Dirac
fermion with the (hidden duality) symmetries appearing in the toroidal
compactification down to 3 space-time dimensions. Next, we investigate how the
fermions (with spin 1/2 or 3/2) fit in the conjecture for hidden over-extended
symmetry G++. Finally, in the context of G+++ invariant actions, we derive all
the possible signatures for all the GB++ theories that can be obtained from the
conventional one (1,D-1) by "dualities" generated by Weyl reflections. This
generalizes the results obtained for E8++.Comment: Ph.D. Thesis, Universite Libre de Bruxelles, June 2006 (232 pages
Cosmological billiards and oxidation
We show how the properties of the cosmological billiards provide useful
information (spacetime dimension and -form spectrum) on the oxidation
endpoint of the oxidation sequence of gravitational theories. We compare this
approach to the other available methods: subgroups and the
superalgebras of dualities.Comment: To appear in the Proceedings of the 27th Johns Hopkins Workshop and
in the Proceedings of the 36th International Symposium Ahrenshoop; v2: minor
error correcte
Hyperbolic Kac Moody Algebras and Einstein Billiards
We identify the hyperbolic Kac Moody algebras for which there exists a
Lagrangian of gravity, dilatons and -forms which produces a billiard that
can be identified with their fundamental Weyl chamber. Because of the
invariance of the billiard upon toroidal dimensional reduction, the list of
admissible algebras is determined by the existence of a Lagrangian in three
space-time dimensions, where a systematic analysis can be carried out since
only zero-forms are involved. We provide all highest dimensional parent
Lagrangians with their full spectrum of -forms and dilaton couplings. We
confirm, in particular, that for the rank 10 hyperbolic algebra, , also known as the dual of , the
maximally oxidized Lagrangian is 9 dimensional and involves besides gravity, 2
dilatons, a 2-form, a 1-form and a 0-form.Comment: 33 page
Describing general cosmological singularities in Iwasawa variables
Belinskii, Khalatnikov, and Lifshitz (BKL) conjectured that the description
of the asymptotic behavior of a generic solution of Einstein equations near a
spacelike singularity could be drastically simplified by considering that the
time derivatives of the metric asymptotically dominate (except at a sequence of
instants, in the `chaotic case') over the spatial derivatives. We present a
precise formulation of the BKL conjecture (in the chaotic case) that consists
of basically three elements: (i) we parametrize the spatial metric by
means of \it{Iwasawa variables} ); (ii) we define, at
each spatial point, a (chaotic) \it{asymptotic evolution system} made of
ordinary differential equations for the Iwasawa variables; and (iii) we
characterize the exact Einstein solutions whose asymptotic
behavior is described by a solution of the
previous evolution system by means of a `\it{generalized Fuchsian system}' for
the differenced variables , , and by requiring that and tend to zero on the singularity. We also show that, in spite of the
apparently chaotic infinite succession of `Kasner epochs' near the singularity,
there exists a well-defined \it{asymptotic geometrical structure} on the
singularity : it is described by a \it{partially framed flag}. Our treatment
encompasses Einstein-matter systems (comprising scalar and p-forms), and also
shows how the use of Iwasawa variables can simplify the usual (`asymptotically
velocity term dominated') description of non-chaotic systems.Comment: 50 pages, 4 figure
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Robust Circadian Oscillations in Growing Cyanobacteria Require Transcriptional Feedback
The remarkably stable circadian oscillations of single cyanobacteria enable a population of growing cells to maintain synchrony for weeks. The cyanobacterial pacemaker is a posttranslational regulation (PTR) circuit that generates circadian oscillations in the phosphorylation state of the clock protein KaiC. Layered on top of the PTR is transcriptional-translational feedback regulation (TTR), common to all circadian systems, consisting of a negative feedback loop in which KaiC regulates its own production. We found that the PTR circuit is sufficient to generate oscillations in growing cyanobacteria. However, in the absence of TTR, individual oscillators were less stable and synchrony was not maintained in a population of cells. Experimentally constrained mathematical modeling reproduced sustained oscillations in the PTR circuit alone and demonstrated the importance of TTR for oscillator synchrony.Chemistry and Chemical BiologyMolecular and Cellular BiologyPhysic
Solitons in Five Dimensional Minimal Supergravity: Local Charge, Exotic Ergoregions, and Violations of the BPS Bound
We describe a number of striking features of a class of smooth solitons in
gauged and ungauged minimal supergravity in five dimensions. The solitons are
globally asymptotically flat or asymptotically AdS without any Kaluza-Klein
directions but contain a minimal sphere formed when a cycle pinches off in the
interior of the spacetime. The solutions carry a local magnetic charge and many
have rather unusual ergosurfaces. Perhaps most strikingly, many of the solitons
have more electric charge or, in the asymptotically AdS case, more electric
charge and angular momentum than is allowed by the usual BPS bound. We comment
on, but do not resolve, the new puzzle this raises for AdS/CFT.Comment: 60 pages, 12 figures, 3 table
Non-Einstein geometries in Chiral Gravity
We analyze the asymptotic solutions of Chiral Gravity (Topologically Massive
Gravity at \mu l = 1 with Brown-Henneaux boundary conditions) focusing on
non-Einstein metrics. A class of such solutions admits curvature singularities
in the interior which are reflected as singularities or infinite bulk energy of
the corresponding linear solutions. A non-linear solution is found exactly. The
back-reaction induces a repulsion of geodesics and a shielding of the
singularity by an event horizon but also introduces closed timelike curves.Comment: 11 pages, 3 figures. v2: references and comments on linear stability
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