Exceptional Superconformal Algebras

Reductive W-algebras which are generated by bosonic fields of spin-1, a single spin-2 field and fermionic fields of spin-3/2 are classified. Three new cases are found: a `symplectic' family of superconformal algebras which are extended by $su(2)\oplus sp(n)$, an $N=7$ and an $N=8$ superconformal algebra. The exceptional cases can be viewed as arising a Drinfeld-Sokolov type reduction of the exceptional Lie superalgebras $G(3)$ and $F(4)$, and have an octonionic description. The quantum versions of the superconformal algebras are constructed explicitly in all three cases.Comment: 16 page

Exotic Statistics for Ordinary Particles in Quantum Gravity

Objects exhibiting statistics other than the familiar Bose and Fermi ones are natural in theories with topologically nontrivial objects including geons, strings, and black holes. It is argued here from several viewpoints that the statistics of ordinary particles with which we are already familiar are likely to be modified due to quantum gravity effects. In particular, such modifications are argued to be present in loop quantum gravity and in any theory which represents spacetime in a fundamentally piecewise-linear fashion. The appearance of unusual statistics may be a generic feature (such as the deformed position-momentum uncertainty relations and the appearance of a fundamental length scale) which are to be expected in any theory of quantum gravity, and which could be testable.Comment: Awarded an honourable mention in the 2008 Gravity Research Foundation Essay Competitio

Low-Energy Effective Action in Non-Perturbative Electrodynamics in Curved Spacetime

We study the heat kernel for the Laplace type partial differential operator acting on smooth sections of a complex spin-tensor bundle over a generic $n$-dimensional Riemannian manifold. Assuming that the curvature of the U(1) connection (that we call the electromagnetic field) is constant we compute the first two coefficients of the non-perturbative asymptotic expansion of the heat kernel which are of zero and the first order in Riemannian curvature and of arbitrary order in the electromagnetic field. We apply these results to the study of the effective action in non-perturbative electrodynamics in four dimensions and derive a generalization of the Schwinger's result for the creation of scalar and spinor particles in electromagnetic field induced by the gravitational field. We discover a new infrared divergence in the imaginary part of the effective action due to the gravitational corrections, which seems to be a new physical effect.Comment: LaTeX, 42 page

An accurate equation of state for the one component plasma in the low coupling regime

An accurate equation of state of the one component plasma is obtained in the low coupling regime $0 \leq \Gamma \leq 1$. The accuracy results from a smooth combination of the well-known hypernetted chain integral equation, Monte Carlo simulations and asymptotic analytical expressions of the excess internal energy $u$. In particular, special attention has been brought to describe and take advantage of finite size effects on Monte Carlo results to get the thermodynamic limit of $u$. This combined approach reproduces very accurately the different plasma correlation regimes encountered in this range of values of $\Gamma$. This paper extends to low $\Gamma$'s an earlier Monte Carlo simulation study devoted to strongly coupled systems for $1 \leq \Gamma \leq 190$ ({J.-M. Caillol}, {J. Chem. Phys.} \textbf{111}, 6538 (1999)). Analytical fits of $u(\Gamma)$ in the range $0 \leq \Gamma \leq 1$ are provided with a precision that we claim to be not smaller than $p= 10^{-5}$. HNC equation and exact asymptotic expressions are shown to give reliable results for $u(\Gamma)$ only in narrow $\Gamma$ intervals, i.e. $0 \leq \Gamma \lesssim 0.5$ and $0 \leq \Gamma \lesssim 0.3$ respectively

Semiclassical thermodynamics of scalar fields

We present a systematic semiclassical procedure to compute the partition function for scalar field theories at finite temperature. The central objects in our scheme are the solutions of the classical equations of motion in imaginary time, with spatially independent boundary conditions. Field fluctuations -- both field deviations around these classical solutions, and fluctuations of the boundary value of the fields -- are resummed in a Gaussian approximation. In our final expression for the partition function, this resummation is reduced to solving certain ordinary differential equations. Moreover, we show that it is renormalizable with the usual 1-loop counterterms.Comment: 24 pages, 5 postscript figure

Incremental elasticity for array databases

Relational databases benefit significantly from elasticity, whereby they execute on a set of changing hardware resources provisioned to match their storage and processing requirements. Such flexibility is especially attractive for scientific databases because their users often have a no-overwrite storage model, in which they delete data only when their available space is exhausted. This results in a database that is regularly growing and expanding its hardware proportionally. Also, scientific databases frequently store their data as multidimensional arrays optimized for spatial querying. This brings about several novel challenges in clustered, skew-aware data placement on an elastic shared-nothing database. In this work, we design and implement elasticity for an array database. We address this challenge on two fronts: determining when to expand a database cluster and how to partition the data within it. In both steps we propose incremental approaches, affecting a minimum set of data and nodes, while maintaining high performance. We introduce an algorithm for gradually augmenting an array database's hardware using a closed-loop control system. After the cluster adds nodes, we optimize data placement for n-dimensional arrays. Many of our elastic partitioners incrementally reorganize an array, redistributing data only to new nodes. By combining these two tools, the scientific database efficiently and seamlessly manages its monotonically increasing hardware resources.Intel Corporation (Science and Technology Center for Big Data

The Origin of B-Type Runaway Stars: Non-LTE Abundances as a Diagnostic

There are two accepted mechanisms to explain the origin of runaway OB-type stars: the Binary Supernova Scenario (BSS), and the Cluster Ejection Scenario (CES). In the former, a supernova explosion within a close binary ejects the secondary star, while in the latter close multi-body interactions in a dense cluster cause one or more of the stars to be ejected from the region at high velocity. Both mechanisms have the potential to affect the surface composition of the runaway star. TLUSTY non-LTE model atmosphere calculations have been used to determine atmospheric parameters and carbon, nitrogen, magnesium and silicon abundances for a sample of B-type runaways. These same analytical tools were used by Hunter et al. (2009) for their analysis of 50 B-type open cluster Galactic stars (i.e. non-runaways). Effective temperatures were deduced using the silicon-ionization balance technique, surface gravities from Balmer line profiles and microturbulent velocities derived using the Si spectrum. The runaways show no obvious abundance anomalies when compared with stars in the open clusters. The runaways do show a spread in composition which almost certainly reflects the Galactic abundance gradient and a range in the birthplaces of the runaways in the Galactic disk. Since the observed Galactic abundance gradients of C, N, Mg and Si are of a similar magnitude, the abundance ratios (e.g., N/Mg) are, as obtained, essentially uniform across the sample

Conformal Scalar Propagation on the Schwarzschild Black-Hole Geometry

The vacuum activity generated by the curvature of the Schwarzschild black-hole geometry close to the event horizon is studied for the case of a massless, conformal scalar field. The associated approximation to the unknown, exact propagator in the Hartle-Hawking vacuum state for small values of the radial coordinate above $r = 2M$ results in an analytic expression which manifestly features its dependence on the background space-time geometry. This approximation to the Hartle-Hawking scalar propagator on the Schwarzschild black-hole geometry is, for that matter, distinct from all other. It is shown that the stated approximation is valid for physical distances which range from the event horizon to values which are orders of magnitude above the scale within which quantum and backreaction effects are comparatively pronounced. An expression is obtained for the renormalised $$ in the Hartle-Hawking vacuum state which reproduces the established results on the event horizon and in that segment of the exterior geometry within which the approximation is valid. In contrast to previous results the stated expression has the superior feature of being entirely analytic. The effect of the manifold's causal structure to scalar propagation is also studied.Comment: 34 pages, 2 figures. Published on line on October 16, 2009 and due to appear in print in Gen.Rel.Gra