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

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 $p$-form spectrum) on the oxidation endpoint of the oxidation sequence of gravitational theories. We compare this approach to the other available methods: $GL(n,R)$ 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 $p$-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 $p$-forms and dilaton couplings. We confirm, in particular, that for the rank 10 hyperbolic algebra, $CE_{10} = A_{15}^{(2)\wedge}$, also known as the dual of $B_8^{\wedge\wedge}$, 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 $g_{ij}$ by means of \it{Iwasawa variables} $\beta^a, {\cal N}^a{}_i$); (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 $\beta, {\cal{N}}$ whose asymptotic behavior is described by a solution $\beta_{[0]}, {\cal N}_{[0]}$ of the previous evolution system by means of a `\it{generalized Fuchsian system}' for the differenced variables $\bar \beta = \beta - \beta_{[0]}$, $\bar {\cal N} = {\cal N} - {\cal N}_{[0]}$, and by requiring that $\bar \beta$ and $\bar {\cal N}$ 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

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 (Sect.2) adde