Supersymmetry of a different kind

Valenzuela, M (Valenzuela, Mauricio). Univ Talca, Inst Matemat & Fis, Talca, ChileA local supersymmetric action for a (2+1)-dimensional system including gravity, the electromagnetic field and a Dirac spin-1/2 field is presented. The action is a Chern-Simons form for a connection of the OSp(2|2) group. All the fields enter as parts of the connection, that transforms in the adjoint representation of the gauge group. The system is off-shell invariant under local (gauge) supersymmetry. Although the supersymmetry is locally realized, there is no spin-3/2 gravitino, and is therefore not supergravity. The fields do not necessarily form supersymmetric doublets of equal mass, and moreover, the fermion may acquire mass through the coupling with geometry, while the bosons - the U(1) field and the spin connection - remain massless

Couplings between Chern-Simons gravities and 2p-branes

The interaction between Chern-Simons (CS) theories and localized external sources (2p-branes) is analyzed. This interaction generalizes the minimal coupling between a point charge (0-brane) and a gauge connection. The external currents that define the 2p-branes are covariantly constant (D-2p-1)-forms coupled to (2p-1) CS forms. The general expression for the sources --charged with respect to the corresponding gauge algebra-- is presented, focusing on two special cases: 0-branes and (D-3)-branes. In any dimension, 0-branes are constructed as topological defects produced by a surface deficit of (D-2)-sphere in AdS space, and they are not constant curvature spaces for D>3. They correspond to dimensionally continued black holes with negative mass. On the other hand, in the case of CS (super) gravities, the (D-3)-branes are naked conical singularities (topological defects) obtained by identification of points with a Killing vector. In 2+1 dimensions, extremal spinning branes of this type are BPS states. Stable (D-3)-branes are shown to exist also in higher dimensions, as well. Classical field equations are also discussed and in the presence of sources there is a large number of inequivalent and disconnected sectors in solution space.Comment: 29 pages, no figures; version accepted in PRD; extended introduction and several references added; some sections have been reorganized and several minor corrections mad

Quantum Degenerate Systems

Degenerate dynamical systems are characterized by symplectic structures whose rank is not constant throughout phase space. Their phase spaces are divided into causally disconnected, nonoverlapping regions such that there are no classical orbits connecting two different regions. Here the question of whether this classical disconnectedness survives quantization is addressed. Our conclusion is that in irreducible degenerate systems --in which the degeneracy cannot be eliminated by redefining variables in the action--, the disconnectedness is maintained in the quantum theory: there is no quantum tunnelling across degeneracy surfaces. This shows that the degeneracy surfaces are boundaries separating distinct physical systems, not only classically, but in the quantum realm as well. The relevance of this feature for gravitation and Chern-Simons theories in higher dimensions cannot be overstated.Comment: 18 pages, no figure

Optical Properties of a \theta-Vacuum

Chern-Simons (CS) forms generalize the minimal coupling between gauge potentials and point charges, to sources represented by charged extended objects (branes). The simplest example of such a CS-brane coupling is a domain wall coupled to the electromagnetic CS three-form. This describes a topologically charged interface where the CS form AdA is supported, separating two three-dimensional spatial regions in 3+1 spacetime. Electrodynamics at either side of the brane is described by the same Maxwell's equations, but those two regions have different vacua, characterized by a different value of the \theta-parameter multiplying the Pontryagin form F ^ F. The \theta-term is the abelian version of the concept introduced by 't Hooft for the resolution of the U(1) problem in QCD. We point out that CS-generalized classical electrodynamics shows new phenomena when two neighboring regions with different \theta-vacua are present. These topological effects result from surface effects induced by the boundary and we explore the consequences of such boundary effects for the propagation of the electromagnetic field in Maxwell theory. Several features, including optical and electrostatic/magnetostatic responses, which may be observable in condensed matter systems, like topological insulators, are discussed.Comment: 11 pages, no figure

Effect of waste glass (TV/PC cathodic tube and screen) on technological properties and sintering behaviour of porcelain stoneware tiles

In the present work, the effects of TV and PC cathodic tube and screen glasses additions (5 and 10 wt.%) to a porcelain stoneware body, in replacement of feldspar, were evaluated simulating the tilemaking process. The presence of glass allows to preserve good technological and mechanical properties, complying with the latest requirements of the industrial practice. The sintering pattern of the glass-added bodies, evaluated by hot stage microscopy, is modified according to the different glass amount and typology; in particular, cathodic tube glass when present at 5 wt.% brings about a lowering of the maximum densification temperature and of the activation energy

Black Hole Entropy and the Dimensional Continuation of the Gauss-Bonnet Theorem

The Euclidean black hole has topology $\Re^2 \times {\cal S}^{d-2}$. It is shown that -in Einstein's theory- the deficit angle of a cusp at any point in $\Re^2$ and the area of the ${\cal S}^{d-2}$ are canonical conjugates. The black hole entropy emerges as the Euler class of a small disk centered at the horizon multiplied by the area of the ${\cal S}^{d-2}$ there.These results are obtained through dimensional continuation of the Gauss-Bonnet theorem. The extension to the most general action yielding second order field equations for the metric in any spacetime dimension is given.Comment: 7 pages, RevTe

A fixed-time second order sliding mode observer for a class of nonlinear systems

This paper presents a second order fixed time sliding mode observer based on an extension of the super-twisting algorithm. This observer can be applied to a class of nonlinear system with a block-wise representation. The block structure provides a straightforward form to the application of the proposed second order sliding mode algorithm, yielding to finite-time convergence with a settling time independent to the system initial conditions. Finally, as numerical simulation example, the case of a linear induction motor is studied, exposing the efficiency and feasibility of the proposal

Violation of Energy Bounds in Designer Gravity

We continue our study of the stability of designer gravity theories, where one considers anti-de Sitter gravity coupled to certain tachyonic scalars with boundary conditions defined by a smooth function W. It has recently been argued there is a lower bound on the conserved energy in terms of the global minimum of W, if the scalar potential arises from a superpotential P and the scalar reaches an extremum of P at infinity. We show, however, there are superpotentials for which these bounds do not hold.Comment: 16 pages, 4 figures, v2: discussion of vacuum decay included, typos corrected, reference adde

Water activated ionic conduction in cross-linked polyelectrolytes

The electrical properties of polyelectrolytes depend on the water concentration of the environment. The behaviour of both conductance and capacitance caused by variations in relative humidity and temperature was investigated by impedance spectroscopy for humidity sensors based on an interpenetrated network of a polymer and a polyelectrolyte. The results were interpreted on the base of the Langmuir and Kelvin equations and two different sensing mechanisms were highlighted for low and high water content