Universal Central Extensions of Gauge Algebras and Groups

We show that the canonical central extension of the group of sections of a Lie group bundle over a compact manifold, constructed in [NW09], is universal. In doing so, we prove universality of the corresponding central extension of Lie algebras in a slightly more general setting.Comment: 9 pages, LaTeX. Changes w.r.t. version 2: minor changes (final version). To appear in J. Reine Angew. Mat

Homotheties and topology of tangent sphere bundles

We prove a Theorem on homotheties between two given tangent sphere bundles $S_rM$ of a Riemannian manifold $M,g$ of $\dim\geq 3$, assuming different variable radius functions $r$ and weighted Sasaki metrics induced by the conformal class of $g$. New examples are shown of manifolds with constant positive or with constant negative scalar curvature, which are not Einstein. Recalling results on the associated almost complex structure $I^G$ and symplectic structure ${\omega}^G$ on the manifold $TM$, generalizing the well-known structure of Sasaki by admitting weights and connections with torsion, we compute the Chern and the Stiefel-Whitney characteristic classes of the manifolds $TM$ and $S_rM$.Comment: 15 pages, to appear in Journal of Geometr

Dyson processes on the octonion algebra

We consider Brownian motion on symmetric matrices of octonions, and study the law of the spectrum. Due to the fact that the octonion algebra is nonassociative, the dimension of the matrices plays a special role. We provide two specific models on octonions, which give some indication of the relation between the multiplicity of eigenvalues and the exponent in the law of the spectrum

Distribution of satellite galaxies in high redshift groups

We use galaxy groups at redshifts between 0.4 and 1.0 selected from the Great Observatories Origins Deep Survey (GOODS) to study the color-morphological properties of satellite galaxies, and investigate possible alignment between the distribution of the satellites and the orientation of their central galaxy. We confirm the bimodal color and morphological type distribution for satellite galaxies at this redshift range: the red and blue classes corresponds to the early and late morphological types respectively, and the early-type satellites are on average brighter than the late-type ones. Furthermore, there is a {\it morphological conformity} between the central and satellite galaxies: the fraction of early-type satellites in groups with an early-type central is higher than those with a late-type central galaxy. This effect is stronger at smaller separations from the central galaxy. We find a marginally significant signal of alignment between the major axis of the early-type central galaxy and its satellite system, while for the late-type centrals no significant alignment signal is found. We discuss the alignment signal in the context of shape evolution of groups.Comment: 7 pages, 7 figures, accepted by Ap

On the twisted G/H topological models

The twisted G/H models are constructed as twisted supersymmetric gauged WZW models. We analyze the case of $G=SU(N)$, $H=SU(N_1)\times ...\times SU(N_n)\times U(1)^r$ with $rank\ G =\ rank\ H$, and discuss possible generalizations. We introduce a non-abelian bosonization of the $(1,0)$ ghost system in the adjoint of $H$ and in G/H. By computing chiral anomalies in the latter picture we write the quantum action as a decoupled sum of ``matter", gauge and ghost sectors. The action is also derived in the unbosonized version. We invoke a free field parametrization and extract the space of physical states by computing the cohomology of $Q$ , the sum of the BRST gauge-fixing charge and the twisted supersymmetry charge. For a given $G$ we briefly discuss the relation between the various G/H models corresponding to different choices of $H$. The choice $H=G$ corresponds to the topological G/G theory.Comment: 27 page

A Theorem on the origin of Phase Transitions

For physical systems described by smooth, finite-range and confining microscopic interaction potentials V with continuously varying coordinates, we announce and outline the proof of a theorem that establishes that unless the equipotential hypersurfaces of configuration space \Sigma_v ={(q_1,...,q_N)\in R^N | V(q_1,...,q_N) = v}, v \in R, change topology at some v_c in a given interval [v_0, v_1] of values v of V, the Helmoltz free energy must be at least twice differentiable in the corresponding interval of inverse temperature (\beta(v_0), \beta(v_1)) also in the N -> \infty$limit. Thus the occurrence of a phase transition at some \beta_c =\beta(v_c) is necessarily the consequence of the loss of diffeomorphicity among the {\Sigma_v}_{v < v_c}$ and the {\Sigma_v}_{v > v_c}, which is the consequence of the existence of critical points of V on \Sigma_{v=v_c}, that is points where \nabla V=0.Comment: 10 pages, Statistical Mechanics, Phase Transitions, General Theory. Phys. Rev. Lett., in pres

Connecting geodesics and security of configurations in compact locally symmetric spaces

A pair of points in a riemannian manifold makes a secure configuration if the totality of geodesics connecting them can be blocked by a finite set. The manifold is secure if every configuration is secure. We investigate the security of compact, locally symmetric spaces.Comment: 27 pages, 2 figure

Physical States in G/G Models and 2d Gravity

An analysis of the BRST cohomology of the G/G topological models is performed for the case of $A_1^{(1)}$. Invoking a special free field parametrization of the various currents, the cohomology on the corresponding Fock space is extracted. We employ the singular vector structure and fusion rules to translate the latter into the cohomology on the space of irreducible representations. Using the physical states we calculate the characters and partition function, and verify the index interpretation. We twist the energy-momentum tensor to establish an intriguing correspondence between the ${SL(2)\over SL(2)}$ model with level $k={p\over q}-2$ and $(p,q)$ models coupled to gravity.Comment: 42 page

Chalcone-based Selective Inhibitors of a C4 Plant Key Enzyme as Novel Potential Herbicides

Weeds are a challenge for global food production due to their rapidly evolving resistance against herbicides. We have identified chalcones as selective inhibitors of phosphoenolpyruvate carboxylase (PEPC), a key enzyme for carbon fixation and biomass increase in the C4 photosynthetic pathway of many of the world’s most damaging weeds. In contrast, many of the most important crop plants use C3 photosynthesis. Here, we show that 2′,3′,4′,3,4-Pentahydroxychalcone (IC50 = 600 nM) and 2′,3′,4′-Trihydroxychalcone (IC50 = 4.2 μM) are potent inhibitors of C4 PEPC but do not affect C3 PEPC at a same concentration range (selectivity factor: 15–45). Binding and modeling studies indicate that the active compounds bind at the same site as malate/aspartate, the natural feedback inhibitors of the C4 pathway. At the whole plant level, both substances showed pronounced growth-inhibitory effects on the C4 weed Amaranthus retroflexus, while there were no measurable effects on oilseed rape, a C3 plant. Growth of selected soil bacteria was not affected by these substances. Our chalcone compounds are the most potent and selective C4 PEPC inhibitors known to date. They offer a novel approach to combat C4 weeds based on a hitherto unexplored mode of allosteric inhibition of a C4 plant key enzyme