Noncommutative vector bundles over fuzzy CP^N and their covariant derivatives

We generalise the construction of fuzzy CP^N in a manner that allows us to access all noncommutative equivariant complex vector bundles over this space. We give a simplified construction of polarization tensors on S^2 that generalizes to complex projective space, identify Laplacians and natural noncommutative covariant derivative operators that map between the modules that describe noncommuative sections. In the process we find a natural generalization of the Schwinger-Jordan construction to su(n) and identify composite oscillators that obey a Heisenberg algebra on an appropriate Fock space.Comment: 34 pages, v2 contains minor corrections to the published versio

X-Ray and UV Orbital Phase Dependence in LMC X-3

The black-hole binary LMC X-3 is known to be variable on time scales of days to years. We investigate X-ray and ultraviolet variability in the system as a function of the 1.7 day binary phase using a 6.4 day observation with the Rossi X-ray Timing Explorer (RXTE) from December 1998. An abrupt 14% flux decrease, lasting nearly an entire orbit, is followed by a return to previous flux levels. This behavior occurs twice, at nearly the same binary phase, but it is not present in consecutive orbits. When the X-ray flux is at lower intensity, a periodic amplitude modulation of 7% is evident in data folded modulo the orbital period. The higher intensity data show weaker correlation with phase. This is the first report of X-ray variability at the orbital period of LMC X-3. Archival RXTE observations of LMC X--3 during a high flux state in December 1996 show similar phase dependence. An ultraviolet light curve obtained with the High Speed Photometer aboard the Hubble Space Telescope shows orbital modulation consistent with that in the optical, caused by the ellipsoidal variation of the spatially deformed companion. The X-ray spectrum of LMC X-3 can be acceptably represented by a phenomenological disk-black-body plus a power law. Changes in the spectrum of LMC X-3 during our observations are compatible with earlier observations during which variations in the 2-10 keV flux are tracked closely by the disk geometry spectral model parameter.Comment: 11 pages, 7 figures, ApJ in pres

On Effective Constraints for the Riemann-Lanczos System of Equations

There have been conflicting points of view concerning the Riemann--Lanczos problem in 3 and 4 dimensions. Using direct differentiation on the defining partial differential equations, Massa and Pagani (in 4 dimensions) and Edgar (in dimensions n > 2) have argued that there are effective constraints so that not all Riemann tensors can have Lanczos potentials; using Cartan's criteria of integrability of ideals of differential forms Bampi and Caviglia have argued that there are no such constraints in dimensions n < 5, and that, in these dimensions, all Riemann tensors can have Lanczos potentials. In this paper we give a simple direct derivation of a constraint equation, confirm explicitly that known exact solutions of the Riemann-Lanczos problem satisfy it, and argue that the Bampi and Caviglia conclusion must therefore be flawed. In support of this, we refer to the recent work of Dolan and Gerber on the three dimensional problem; by a method closely related to that of Bampi and Caviglia, they have found an 'internal identity' which we demonstrate is precisely the three dimensional version of the effective constraint originally found by Massa and Pagani, and Edgar.Comment: 9pages, Te

1D Potts, Yang-Lee Edges and Chaos

It is known that the (exact) renormalization transformations for the one-dimensional Ising model in field can be cast in the form of a logistic map f(x) = 4 x (1 - x) with x a function of the Ising couplings. Remarkably, the line bounding the region of chaotic behaviour in x is precisely that defining the Yang-Lee edge singularity in the Ising model. In this paper we show that the one dimensional q-state Potts model for q greater than or equal to 1 also displays such behaviour. A suitable combination of Potts couplings can again be used to define an x satisfying f(x) = 4 x (1 -x). The Yang-Lee zeroes no longer lie on the unit circle in the complex z = exp (h) plane, but their locus is still reproduced by the boundary of the chaotic region in the logistic map.Comment: 6 pages, no figure

Yangians in Deformed Super Yang-Mills Theories

We discuss the integrability structure of deformed, four-dimensional N=4 super Yang-Mills theories using Yangians. We employ a recent procedure by Beisert and Roiban that generalizes the beta deformation of Lunin and Maldacena to produce N=1 superconformal gauge theories, which have the superalgebra SU(2,2|1)xU(1)xU(1). The deformed theories, including those with the more general twist, were shown to have retained their integrable structure. Here we examine the Yangian algebra of these deformed theories. In a five field subsector, we compute the two cases of SU(2)xU(1)xU(1)xU(1) and SU(2|1)xU(1)xU(1) as residual symmetries of SU(2,2|1)xU(1)xU(1). We compute a twisted coproduct for these theories, and show that only for the residual symmetry do we retain the standard coproduct. The twisted coproduct thus provides a method for symmetry breaking. However, the full Yangian structure of SU(2|3) is manifest in our subsector, albeit with twisted coproducts, and provides for the integrability of the theory.Comment: 17 page

Transcriptional profiling of Arabidopsis root hairs and pollen defines an apical cell growth signature

Background: Current views on the control of cell development are anchored on the notion that phenotypes are defined by networks of transcriptional activity. The large amounts of information brought about by transcriptomics should allow the definition of these networks through the analysis of cell-specific transcriptional signatures. Here we test this principle by applying an analogue to comparative anatomy at the cellular level, searching for conserved transcriptional signatures, or conserved small gene-regulatory networks (GRNs) on root hairs (RH) and pollen tubes (PT), two filamentous apical growing cells that are a striking example of conservation of structure and function in plants.Results: We developed a new method for isolation of growing and mature root hair cells, analysed their transcriptome by microarray analysis, and further compared it with pollen and other single cell transcriptomics data. Principal component analysis shows a statistical relation between the datasets of RHs and PTs which is suggestive of a common transcriptional profile pattern for the apical growing cells in a plant, with overlapping profiles and clear similarities at the level of small GTPases, vesicle-mediated transport and various specific metabolic responses. Furthermore, cis-regulatory element analysis of co-regulated genes between RHs and PTs revealed conserved binding sequences that are likely required for the expression of genes comprising the apical signature. This included a significant occurrence of motifs associated to a defined transcriptional response upon anaerobiosis.Conclusions: Our results suggest that maintaining apical growth mechanisms synchronized with energy yielding might require a combinatorial network of transcriptional regulation. We propose that this study should constitute the foundation for further genetic and physiological dissection of the mechanisms underlying apical growth of plant cells

A Link Representation for Gravity Amplitudes

We derive a link representation for all tree amplitudes in N=8 supergravity, from a recent conjecture by Cachazo and Skinner. The new formula explicitly writes amplitudes as contour integrals over constrained link variables, with an integrand naturally expressed in terms of determinants, or equivalently tree diagrams. Important symmetries of the amplitude, such as supersymmetry, parity and (partial) permutation invariance, are kept manifest in the formulation. We also comment on rewriting the formula in a GL(k)-invariant manner, which may serve as a starting point for the generalization to possible Grassmannian contour integrals.Comment: 11 page

Anomalous Dimensions of Non-Chiral Operators from AdS/CFT

Non-chiral operators with positive anomalous dimensions can have interesting applications to supersymmetric model building. Motivated by this, we develop a new method for obtaining the anomalous dimensions of non-chiral double-trace operators in N=1 superconformal field theories (SCFTs) with weakly-coupled AdS duals. Via the Hamiltonian formulation of AdS/CFT, we show how to directly compute the anomalous dimension as a bound state energy in the gravity dual. This simplifies previous approaches based on the four-point function and the OPE. We apply our method to a class of effective AdS5 supergravity models, and we find that the binding energy can have either sign. If such models can be UV completed, they will provide the first calculable examples of SCFTs with positive anomalous dimensions.Comment: 38 pages, 2 figures, refs adde

The Yangian of sl(n|m) and the universal R-matrix

In this paper we study Yangians of sl(n|m) superalgebras. We derive the universal R-matrix and evaluate it on the fundamental representation obtaining the standard Yang R-matrix with unitary dressing factors. For m=0, we directly recover up to a CDD factor the well-known S-matrices for relativistic integrable models with su(N) symmetry. Hence, the universal R-matrix found provides an abstract plug-in formula, which leads to results obeying fundamental physical constraints: crossing symmetry, unitrarity and the Yang-Baxter equation. This implies that the Yangian double unifies all desired symmetries into one algebraic structure. In particular, our analysis is valid in the case of sl(n|n), where one has to extend the algebra by an additional generator leading to the algebra gl(n|n). We find two-parameter families of scalar factors in this case and provide a detailed study for gl(1|1).Comment: 24 pages, 2 figure