Sophie de Buyl

Robust Circadian Oscillations in Growing Cyanobacteria Require Transcriptional Feedback

Keeping in Synch Although it differs from mammalian clocks, the circadian clock of cyanobacteria is a valuable model for understanding how such clocks function. At the heart of the cyanobacterial clock is a posttranslational regulation (PTR) circuit in which the phosphorylation of the clock protein KaiC oscillates. This circuit is apparently sufficient for generating rhythms, but it is connected to a transcriptional-translational (TTR) feedback loop more similar to the one that functions in mammals. This TTR loop is, at least in some conditions, dispensable. To understand the role of the TTR circuit, Teng et al. (p. 737) engineered cyanobacteria so that the circadian behavior of individual cells in a population of growing cells could be monitored. Cells engineered to lack the TTR mechanism had rhythmic clocks but fell out of synch with the other cells in a population over time. The experimental results together with mathematical modeling indicate that the TTR mechanism is important to allow cells to robustly stay in rhythm with one another in the absence of synchronizing external cues. The cyanobacterial clock uses one circuit for rhythms and a second circuit for intercellular synchronous oscillations. 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.

Extended E8 invariance of 11-dimensional supergravity

The hyperbolic Kac-Moody algebra E10 has repeatedly been suggested to play a crucial role in the symmetry structure of M-theory. Recently, following the analysis of the asymptotic behaviour of the supergravity fields near a cosmological singularity, this question has received a new impulse. It has been argued that one way to exhibit the symmetry was to rewrite the supergravity equations as the equations of motion of the non-linear sigma model E10/K(E10). This attempt, in line with the established result that the scalar fields which appear in the toroidal compactification down to three spacetime dimensions form the coset E8/SO({16}), was verified for the first bosonic levels in a level expansion of the theory. We show that the same features remain valid when one includes the gravitino field.

The curious case of null warped space

We initiate a comprehensive study of a set of solutions of topologically massive gravity known as null warped anti-de Sitter spacetimes. These are pp-wave extensions of three-dimensional anti-de Sitter space. We first perform a careful analysis of the linearized stability of black holes in these spacetimes. We find two qualitatively different types of solutions to the linearized equations of motion: the first set has an exponential time dependence, the second — a polynomial time dependence. The solutions polynomial in time induce severe pathologies and moreover survive at the non-linear level. In order to make sense of these geometries, it is thus crucial to impose appropriate boundary conditions. We argue that there exists a consistent set of boundary conditions that allows us to reject the above pathological modes from the physical spectrum. The asymptotic symmetry group associated to these boundary conditions consists of a centrally-extended Virasoro algebra. Using this central charge we can account for the entropy of the black holes via Cardy’s formula. Finally, we note that the black hole spectrum is chiral and prove a Birkoff theorem showing that there are no other stationary axisymmetric black holes with the specified asymptotics. We extend most of the analysis to a larger family of pp-wave black holes which are related to Schrödinger spacetimes with critical exponent z.

G2 dualities in D = 5 supergravity and black strings

Five-dimensional minimal supergravity dimensionally reduced on two commuting Killing directions gives rise to a G2 coset model. The symmetry group of the coset model can be used to generate new solutions by applying group transformations on a seed solution. We show that on a general solution the generators belonging to the Cartan and nilpotent subalgebras of G2 act as scaling and gauge transformations, respectively. The remaining generators of G2 form a subalgebra that can be used to generate non-trivial charges. We use these generators to generalize the five-dimensional Kerr string in a number of ways. In particular, we construct the spinning electric and spinning magnetic black strings of five-dimensional minimal supergravity. We analyze physical properties of these black strings and study their thermodynamics. We also explore their relation to black rings.

Hidden symmetries and Dirac fermions

In this paper, two things are done. First, we analyse the compatibility of Dirac fermions with the hidden duality symmetries which appear in the toroidal compactification of gravitational theories down to three spacetime dimensions. We show that the Pauli couplings to the p-forms can be adjusted, for all simple (split) groups, so that the fermions transform in a representation of the maximal compact subgroup of the duality group G in three dimensions. Second, we investigate how the Dirac fermions fit in the conjectured hidden overextended symmetry G++. We show compatibility with this symmetry up to the same level as in the pure bosonic case. We also investigate the BKL behaviour of the Einstein–Dirac-p-form systems and provide a group theoretical interpretation of the Belinskii–Khalatnikov result that the Dirac field removes chaos.

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, CE10=A15(2)∧, also known as the dual of B8∧∧, the maximally oxidized Lagrangian is nine-dimensional and involves besides gravity, 2 dilatons, a 2-form, a 1-form, and a 0-form.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, CE10=A15(2)∧, also known as the dual of B8∧∧, the maximally oxidized Lagrangian is nine-dimensional and involves besides gravity, 2 dilatons, a 2-form, a 1-form, and a 0-form.

Asymptotic symmetries of Schrödinger spacetimes

We discuss the asymptotic symmetry algebra of the Schrodinger -invariant metrics in d+3 dimensions and its realization on finite temperature solutions of gravity coupled to matter fields. These solutions have been proposed as gravity backgrounds dual to non-relativistic CFTs with critical exponent z in d space dimensions. It is known that the Schrodinger algebra possesses an infinite-dimensional extension, the Schrodinger-Virasoro algebra. However, we show that the asymptotic symmetry algebra of Schrodinger spacetimes is only isomorphic to the exact symmetry group of the background. It is possible to construct from first principles finite and integrable charges that infinite-dimensionally extend the Schrodinger algebra but these charges are not correctly represented via a Dirac bracket. We briefly comment on the extension of our analysis to spacetimes with Lifshitz symmetry.

Holography For a De Sitter-Esque Geometry

Warped dS3 arises as a solution to topologically massive gravity (TMG) with positive cosmological constant +1/ℓ2 and Chern-Simons coefficient 1/μ in the region μ2ℓ2 < 27. It is given by a real line fibration over two-dimensional de Sitter space and is equivalent to the rotating Nariai geometry at fixed polar angle. We study the thermodynamic and asymptotic structure of a family of geometries with warped dS3 asymptotics. Interestingly, these solutions have both a cosmological horizon and an internal one, and their entropy is unbounded from above unlike black holes in regular de Sitter space. The asymptotic symmetry group resides at future infinity and is given by a semi-direct product of a Virasoro algebra and a current algebra. The right moving central charge vanishes when μ2ℓ2 = 27/5. We discuss the possible holographic interpretation of these de Sitter-esque spacetimes.

A general black string and its microscopics

Using G2(2) dualities we construct the most general black string solution of minimal five-dimensional ungauged supergravity. The black string has five independent parameters, namely, the magnetic one-brane charge, smeared electric zero-brane charge, boost along the string direction, energy above the BPS bound, and rotation in the transverse space. In one extremal limit it reduces to the three parameter supersymmetric string of five-dimensional minimal supergravity; in another extremal limit it reduces to the three parameter non-supersymmetric non-rotating extremal string of five-dimensional minimal supergravity. It also admits an extremal limit when it has maximal rotation in the four-dimensional transverse space. The decoupling limit of our general black string is a BTZ black hole times a two sphere. The macroscopic entropy of the string is reproduced by the Maldacena-Strominger-Witten CFT in appropriate ranges of the parameters. When the pressureless condition is imposed, our string describes the infinite radius limit of the most general class of black rings of minimal supergravity. We discuss implications our solution has for extremal and non-extremal black rings of minimal supergravity.

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.