Draco -- A Failure of the Tidal Model

We test whether the structural properties of the nearby dwarf spheroidal (dSph) galaxy Draco, a well-studied Milky Way companion, can be reconciled with the suggestion that dSphs are unbound tidal remnants with a large depth extent along the line of sight. In order to apply the observational test of this hypothesis suggested by Klessen & Zhao, we use public photometric data from the Sloan Digital Sky Survey (SDSS) to explore the width of Draco's blue horizontal branch over a range of areas covering 0.06 square degrees to 6.25 square degrees centered on Draco. The SDSS database is the only currently existing database with sufficient depth and area coverage to permit a stringent test of the tidal models. We show that blue horizontal branch stars extend beyond the previously inferred limiting radii of Draco, consistent with the observed absence of a truncated stellar surface density profile of this dSph. We calculate new models for a galaxy without dark matter, using Draco's morphological properties as constraints. The resulting models are unable to reproduce the narrow observed horizontal branch width of Draco, which stays roughly constant regardless of the field of view. We conclude that Draco cannot be the remnant of a tidally disrupted satellite, but is probably strongly dark-matter dominated. (ABSTRACT ABBREVIATED)Comment: 26 pages, 9 figures included, accepted for publication in ApJ, high-resolution version available at http://www.aip.de./~ralf/Publications/p22.abstract.htm

Asymptotic behaviour of two-point functions in multi-species models

We extract the long-distance asymptotic behaviour of two-point correlation functions in massless quantum integrable models containing multi-species excitations. For such a purpose, we extend to these models the method of a large-distance regime re-summation of the form factor expansion of correlation functions. The key feature of our analysis is a technical hypothesis on the large-volume behaviour of the form factors of local operators in such models. We check the validity of this hypothesis on the example of the $SU(3)$-invariant XXX magnet by means of the determinant representations for the form factors of local operators in this model. Our approach confirms the structure of the critical exponents obtained previously for numerous models solvable by the nested Bethe Ansatz.Comment: 45 pages, 1 figur

Maxwell Superalgebras and Abelian Semigroup Expansion

The Abelian semigroup expansion is a powerful and simple method to derive new Lie algebras from a given one. Recently it was shown that the $S$-expansion of $\mathfrak{so}\left( 3,2\right)$ leads us to the Maxwell algebra $\mathcal{M}$. In this paper we extend this result to superalgebras, by proving that different choices of abelian semigroups $S$ lead to interesting $D=4$ Maxwell Superalgebras. In particular, the minimal Maxwell superalgebra $s\mathcal{M}$ and the $N$-extended Maxwell superalgebra $s\mathcal{M}^{\left( N\right) }$ recently found by the Maurer Cartan expansion procedure, are derived alternatively as an $S$-expansion of $\mathfrak{osp}\left( 4|N\right)$. Moreover we show that new minimal Maxwell superalgebras type $s\mathcal{M}_{m+2}$ and their $N$-extended generalization can be obtained using the $S$-expansion procedure.Comment: 31 pages, some clarifications in the abstract,introduction and conclusion, typos corrected, a reference and acknowledgements added, accepted for publication in Nuclear Physics

N=1 Supergravity and Maxwell superalgebras

We present the construction of the $D=4$ supergravity action from the minimal Maxwell superalgebra $s\mathcal{M}_{4}$, which can be derived from the $\mathfrak{osp}\left( 4|1\right)$ superalgebra by applying the abelian semigroup expansion procedure. We show that $N=1$, $D=4$ pure supergravity can be obtained alternatively as the MacDowell-Mansouri like action built from the curvatures of the Maxwell superalgebra $s\mathcal{M}_{4}$. We extend this result to all minimal Maxwell superalgebras type $s\mathcal{M}_{m+2}$. The invariance under supersymmetry transformations is also analized.Comment: 22 pages, published versio

Electromagnetic response and effective gauge theory of graphene in a magnetic field

The electromagnetic response of graphene in a magnetic field is studied, with particular emphasis on the quantum features of its ground state (vacuum). The graphene vacuum, unlike in conventional quantum Hall systems, is a dielectric medium and carries an appreciable amount of electric and magnetic susceptibilities. The dielectric effect grows rapidly with increasing filling factor nu in such a way that reflects the 'relativistic' Landau-level characteristics of graphene as well as its valley and spin degeneracy. A close look into the dielectric function also reveals that the Coulomb interaction is efficiently screened on the scale of the magnetic length, leading to a prominent reduction of the exciton spectra in graphene. In addition, an effective gauge theory of graphene is constructed out of the response. It is pointed out thereby that the electric susceptibility is generally expressed as a ratio of the Hall conductance to the Landau gap.Comment: 9 pages, 3 figures, revtex, corrected typo

On the Weakening of Chromospheric Magnetic Field in Active Regions

Simultaneous measurement of line-of-sight (LOS) magnetic and velocity fields at the photosphere and chromosphere are presented. Fe I line at $\lambda6569$ and $H_{\alpha}$ at $\lambda6563$ are used respectively for deriving the physical parameters at photospheric and chromospheric heights. The LOS magnetic field obtained through the center-of-gravity method show a linear relation between photospheric and chromospheric field for field strengths less than 700 G. But in strong field regions, the LOS magnetic field values derived from $H_{\alpha}$ are much weaker than what one gets from the linear relationship and also from those expected from the extrapolation of the photospheric magnetic field. We discuss in detail the properties of magnetic field observed in $H_{\alpha}$ from the point of view of observed velocity gradients. The bisector analysis of $H_{\alpha}$ Stokes $I$ profiles show larger velocity gradients in those places where strong photospheric magnetic fields are observed. These observations may support the view that the stronger fields diverge faster with height compared to weaker fields.Comment: accepted for publication in Ap

Sklyanin Bracket and Deformation of the Calogero-Moser System

A two-dimensional integrable system being a deformation of the rational Calogero-Moser system is constructed via the symplectic reduction, performed with respect to the Sklyanin algebra action. We explicitly resolve the respective classical equations of motion via the projection method and quantize the system.Comment: 14 pages, no figure

Conformal Sigma Models with Anomalous Dimensions and Ricci Solitons

We present new non-Ricci-flat Kahler metrics with U(N) and O(N) isometries as target manifolds of superconformally invariant sigma models with an anomalous dimension. They are so-called Ricci solitons, special solutions to a Ricci-flow equation. These metrics explicitly contain the anomalous dimension and reduce to Ricci-flat Kahler metrics on the canonical line bundles over certain coset spaces in the limit of vanishing anomalous dimension.Comment: 9 pages, no figure