Affine orbifolds and rational conformal field theory extensions of W_{1+infinity}

Chiral orbifold models are defined as gauge field theories with a finite gauge group $\Gamma$. We start with a conformal current algebra A associated with a connected compact Lie group G and a negative definite integral invariant bilinear form on its Lie algebra. Any finite group $\Gamma$ of inner automorphisms or A (in particular, any finite subgroup of G) gives rise to a gauge theory with a chiral subalgebra $A^{\Gamma}\subset A$ of local observables invariant under $\Gamma$. A set of positive energy $A^{\Gamma}$ modules is constructed whose characters span, under some assumptions on $\Gamma$, a finite dimensional unitary representation of $SL(2,Z)$. We compute their asymptotic dimensions (thus singling out the nontrivial orbifold modules) and find explicit formulae for the modular transformations and hence, for the fusion rules. As an application we construct a family of rational conformal field theory (RCFT) extensions of $W_{1+\infty}$ that appear to provide a bridge between two approaches to the quantum Hall effect.Comment: 64 pages, amste

mm-cluster categories and mm-replicated algebras

Let A be a hereditary algebra over an algebraically closed field. We prove that an exact fundamental domain for the m-cluster category of A is the m-left part of the m-replicated algebra $A^{(m)}$ of A. Moreover, we obtain a one-to-one correspondence between the tilting objects in the m-cluster category (that is, the m-clusters) and those tilting $A^{(m)}$-modules for which all non projective-injective direct summands lie in the m-left part of $A^{(m)}$.Comment: 28 pages, 2 figure

Magneto-mechanical interplay in spin-polarized point contacts

We investigate the interplay between magnetic and structural dynamics in ferromagnetic atomic point contacts. In particular, we look at the effect of the atomic relaxation on the energy barrier for magnetic domain wall migration and, reversely, at the effect of the magnetic state on the mechanical forces and structural relaxation. We observe changes of the barrier height due to the atomic relaxation up to 200%, suggesting a very strong coupling between the structural and the magnetic degrees of freedom. The reverse interplay is weak, i.e. the magnetic state has little effect on the structural relaxation at equilibrium or under non-equilibrium, current-carrying conditions.Comment: 5 pages, 4 figure

Power dissipation in nanoscale conductors: classical, semi-classical and quantum dynamics

Modelling Joule heating is a difficult problem because of the need to introduce correct correlations between the motions of the ions and the electrons. In this paper we analyse three different models of current induced heating (a purely classical model, a fully quantum model and a hybrid model in which the electrons are treated quantum mechanically and the atoms are treated classically). We find that all three models allow for both heating and cooling processes in the presence of a current, and furthermore the purely classical and purely quantum models show remarkable agreement in the limit of high biases. However, the hybrid model in the Ehrenfest approximation tends to suppress heating. Analysis of the equations of motion reveals that this is a consequence of two things: the electrons are being treated as a continuous fluid and the atoms cannot undergo quantum fluctuations. A means for correcting this is suggested

Effective one-body approach to the relativistic two-body problem

The relativistic 2-body problem, much like the non-relativistic one, is reduced to describing the motion of an effective particle in an external field. The concept of a relativistic reduced mass and effective particle energy introduced some 30 years ago to compute relativistic corrections to the Balmer formula in quantum electrodynamics, is shown to work equally well for classical electromagnetic and gravitational interaction. The results for the gravitational 2-body problem have more than academic interest since they apply to the study of binary pulsars that provide precision tests for general relativity. They are compared with recent results derived by other methods.Comment: 9 pages, latex, no figures. Minor amendments, comments, new references and acknowledgments adde

Four Dimensional CFT Models with Rational Correlation Functions

Recently established rationality of correlation functions in a globally conformal invariant quantum field theory satisfying Wightman axioms is used to construct a family of soluble models in 4-dimensional Minkowski space-time. We consider in detail a model of a neutral scalar field $\phi$ of dimension 2. It depends on a positive real parameter c, an analogue of the Virasoro central charge, and admits for all (finite) c an infinite number of conserved symmetric tensor currents. The operator product algebra of $\phi$ is shown to coincide with a simpler one, generated by a bilocal scalar field $V(x_1,x_2)$ of dimension (1,1). The modes of V together with the unit operator span an infinite dimensional Lie algebra $L_V$ whose vacuum (i.e. zero energy lowest weight) representations only depend on the central charge c. Wightman positivity (i.e. unitarity of the representations of $L_V$) is proven to be equivalent to $c \in N$.Comment: 28 pages, LATEX, amsfonts, latexsym. Proposition 2.3, and Conjecture in Sec. 6 are revised. Minor errors are correcte

Phases of 4D Scalar-tensor black holes coupled to Born-Infeld nonlinear electrodynamics

Recent results show that when non-linear electrodynamics is considered the no-scalar-hair theorems in the scalar-tensor theories (STT) of gravity, which are valid for the cases of neutral black holes and charged black holes in the Maxwell electrodynamics, can be circumvented. What is even more, in the present work, we find new non-unique, numerical solutions describing charged black holes coupled to non-linear electrodynamics in a special class of scalar-tensor theories. One of the phases has a trivial scalar field and coincides with the corresponding solution in General Relativity. The other four phases that we find are characterized by the value of the scalar field charge. The causal structure and some aspects of the stability of the solutions have also been studied. For the scalar-tensor theories considered, the black holes have a single, non-degenerate horizon, i.e., their causal structure resembles that of the Schwarzschild black hole. The thermodynamic analysis of the stability of the solutions indicates that a phase transition may occur.Comment: 18 pages, 8 figures, new phases, figures, clarifying remarks and acknowledgements adde