Supersymmetry and homogeneity of M-theory backgrounds

We describe the construction of a Lie superalgebra associated to an arbitrary supersymmetric M-theory background, and discuss some examples. We prove that for backgrounds with more than 24 supercharges, the bosonic subalgebra acts locally transitively. In particular, we prove that backgrounds with more than 24 supersymmetries are necessarily (locally) homogeneous.Comment: 19 pages (Erroneous Section 6.3 removed from the paper.

On the maximal superalgebras of supersymmetric backgrounds

In this note we give a precise definition of the notion of a maximal superalgebra of certain types of supersymmetric supergravity backgrounds, including the Freund-Rubin backgrounds, and propose a geometric construction extending the well-known construction of its Killing superalgebra. We determine the structure of maximal Lie superalgebras and show that there is a finite number of isomorphism classes, all related via contractions from an orthosymplectic Lie superalgebra. We use the structure theory to show that maximally supersymmetric waves do not possess such a maximal superalgebra, but that the maximally supersymmetric Freund-Rubin backgrounds do. We perform the explicit geometric construction of the maximal superalgebra of AdS_4 x S^7 and find that is isomorphic to osp(1|32). We propose an algebraic construction of the maximal superalgebra of any background asymptotic to AdS_4 x S^7 and we test this proposal by computing the maximal superalgebra of the M2-brane in its two maximally supersymmetric limits, finding agreement.Comment: 17 page

Power Utility Maximization in Discrete-Time and Continuous-Time Exponential Levy Models

Consider power utility maximization of terminal wealth in a 1-dimensional continuous-time exponential Levy model with finite time horizon. We discretize the model by restricting portfolio adjustments to an equidistant discrete time grid. Under minimal assumptions we prove convergence of the optimal discrete-time strategies to the continuous-time counterpart. In addition, we provide and compare qualitative properties of the discrete-time and continuous-time optimizers.Comment: 18 pages, to appear in Mathematical Methods of Operations Research. The final publication is available at springerlink.co

Diagnosis of Spinocerebellar Ataxia in the West Indies

Background: Access to medical care in many regions is limited by socioeconomic status, at both the individual and the community level. This report describes the diagnostic process of a family residing on an underserved Caribbean island where routine neurological care is typically addressed by general practitioners, and genetic diagnosis is not available through regular medical channels. The diagnosis and management of neurodegenerative disorders is especially challenging in this setting. Case Report: We diagnosed a family with spinocerebellar ataxia type 3 (SCA3) in an underdeveloped nation with limited access to genetic medicine and no full-time neurologist. Discussion: Molecular diagnosis of the SCAs can be challenging, even in developed countries. In the Caribbean, genetic testing is generally only available at a small number of academic centers. Diagnosis in this family was ultimately made by utilizing an international, pro bono, research-based collaborative process. Although access to appropriate resources, such as speech, physical, and occupational therapies, is limited on this island because of economic and geographical factors, the provision of a diagnosis appeared to be ultimately beneficial for this family. Identification of affected families highlights the need for access to genetic diagnosis in all communities, and can help direct resources where needed

Combinatorial Hopf algebras in quantum field theory I

This manuscript stands at the interface between combinatorial Hopf algebra theory and renormalization theory. Its plan is as follows: Section 1 is the introduction, and contains as well an elementary invitation to the subject. The rest of part I, comprising Sections 2-6, is devoted to the basics of Hopf algebra theory and examples, in ascending level of complexity. Part II turns around the all-important Faa di Bruno Hopf algebra. Section 7 contains a first, direct approach to it. Section 8 gives applications of the Faa di Bruno algebra to quantum field theory and Lagrange reversion. Section 9 rederives the related Connes-Moscovici algebras. In Part III we turn to the Connes-Kreimer Hopf algebras of Feynman graphs and, more generally, to incidence bialgebras. In Section10 we describe the first. Then in Section11 we give a simple derivation of (the properly combinatorial part of) Zimmermann's cancellation-free method, in its original diagrammatic form. In Section 12 general incidence algebras are introduced, and the Faa di Bruno bialgebras are described as incidence bialgebras. In Section 13, deeper lore on Rota's incidence algebras allows us to reinterpret Connes-Kreimer algebras in terms of distributive lattices. Next, the general algebraic-combinatorial proof of the cancellation-free formula for antipodes is ascertained; this is the heart of the paper. The structure results for commutative Hopf algebras are found in Sections 14 and 15. An outlook section very briefly reviews the coalgebraic aspects of quantization and the Rota-Baxter map in renormalization.Comment: 94 pages, LaTeX figures, precisions made, typos corrected, more references adde

N=2 structures on solvable Lie algebras: the c=9 classification

Let G be a finite-dimensional Lie algebra (not necessarily semisimple). It is known that if G is self-dual (that is, if it possesses an invariant metric) then there is a canonical N=1 superconformal algebra associated to its N=1 affinization---that is, it admits an N=1 (affine) Sugawara construction. Under certain additional hypotheses, this N=1 structure admits an N=2 extension. If this is the case, G is said to possess an N=2 structure. It is also known that an N=2 structure on a self-dual Lie algebra G is equivalent to a vector space decomposition G = G_+ \oplus G_- where G_\pm are isotropic Lie subalgebras. In other words, N=2 structures on G are in one-to-one correspondence with Manin triples (G,G_+,G_-). In this paper we exploit this correspondence to obtain a classification of the c=9 N=2 structures on self-dual solvable Lie algebras. In the process we also give some simple proofs for a variety of Lie algebraic results concerning self-dual Lie algebras admitting symplectic or K\"ahler structures.Comment: 49 pages in 2 columns (=25 physical pages), (uufiles-gz-9)'d .dvi file (uses AMSFonts 2.1+). Revision: Added 1 reference, corrected typos, added some more materia

Cosmological hydrodynamical simulations of galaxy clusters: X-ray scaling relations and their evolution

We analyse cosmological hydrodynamical simulations of galaxy clusters to study the X-ray scaling relations between total masses and observable quantities such as X-ray luminosity, gas mass, X-ray temperature, and $Y_{X}$. Three sets of simulations are performed with an improved version of the smoothed particle hydrodynamics GADGET-3 code. These consider the following: non-radiative gas, star formation and stellar feedback, and the addition of feedback by active galactic nuclei (AGN). We select clusters with $M_{500} > 10^{14} M_{\odot} E(z)^{-1}$, mimicking the typical selection of Sunyaev-Zeldovich samples. This permits to have a mass range large enough to enable robust fitting of the relations even at $z \sim 2$. The results of the analysis show a general agreement with observations. The values of the slope of the mass-gas mass and mass-temperature relations at $z=2$ are 10 per cent lower with respect to $z=0$ due to the applied mass selection, in the former case, and to the effect of early merger in the latter. We investigate the impact of the slope variation on the study of the evolution of the normalization. We conclude that cosmological studies through scaling relations should be limited to the redshift range $z=0-1$, where we find that the slope, the scatter, and the covariance matrix of the relations are stable. The scaling between mass and $Y_X$ is confirmed to be the most robust relation, being almost independent of the gas physics. At higher redshifts, the scaling relations are sensitive to the inclusion of AGNs which influences low-mass systems. The detailed study of these objects will be crucial to evaluate the AGN effect on the ICM.Comment: 24 pages, 11 figures, 5 tables, replaced to match accepted versio

Dynamics of intersecting brane systems -- Classification and their applications --

We present dynamical intersecting brane solutions in higher-dimensional gravitational theory coupled to dilaton and several forms. Assuming the forms of metric, form fields, and dilaton field, we give a complete classification of dynamical intersecting brane solutions with/without M-waves and Kaluza-Klein monopoles in eleven-dimensional supergravity. We apply these solutions to cosmology and black holes. It is shown that these give FRW cosmological solutions and in some cases Lorentz invariance is broken in our world. If we regard the bulk space as our universe, we may interpret them as black holes in the expanding universe. We also discuss lower-dimensional effective theories and point out naive effective theories may give us some solutions which are inconsistent with the higher-dimensional Einstein equations.Comment: 44 pages; v2: minor corrections, references adde

The spinorial geometry of supersymmetric backgrounds

We propose a new method to solve the Killing spinor equations of eleven-dimensional supergravity based on a description of spinors in terms of forms and on the Spin(1,10) gauge symmetry of the supercovariant derivative. We give the canonical form of Killing spinors for N=2 backgrounds provided that one of the spinors represents the orbit of Spin(1,10) with stability subgroup SU(5). We directly solve the Killing spinor equations of N=1 and some N=2, N=3 and N=4 backgrounds. In the N=2 case, we investigate backgrounds with SU(5) and SU(4) invariant Killing spinors and compute the associated spacetime forms. We find that N=2 backgrounds with SU(5) invariant Killing spinors admit a timelike Killing vector and that the space transverse to the orbits of this vector field is a Hermitian manifold with an SU(5)-structure. Furthermore, N=2 backgrounds with SU(4) invariant Killing spinors admit two Killing vectors, one timelike and one spacelike. The space transverse to the orbits of the former is an almost Hermitian manifold with an SU(4)-structure and the latter leaves the almost complex structure invariant. We explore the canonical form of Killing spinors for backgrounds with extended, N>2, supersymmetry. We investigate a class of N=3 and N=4 backgrounds with SU(4) invariant spinors. We find that in both cases the space transverse to a timelike vector field is a Hermitian manifold equipped with an SU(4)-structure and admits two holomorphic Killing vector fields. We also present an application to M-theory Calabi-Yau compactifications with fluxes to one-dimension.Comment: Latex, 54 pages, v2: clarifications made and references added. v3: minor changes. v4: minor change