Making the hyper--K\"ahler structure of N=2 quantum string manifest

We show that the Lorentz covariant formulation of N=2 string in a curved space reveals an explicit hyper--K\"ahler structure. Apart from the metric, the superconformal currents couple to a background two--form. By superconformal symmetry the latter is constrained to be holomorphic and covariantly constant and allows one to construct three complex structures obeying a (pseudo)quaternion algebra.Comment: 8 pages, no figures, PACS: 04.60.Ds; 11.30.Pb, Keywords: N=2 string, hyper-K\"ahler geometry. Presentation improved, references added. The version to appear in PR

Supersymmetric Extension of Hopf Maps: N=4 sigma-models and the S^3 -> S^2 Fibration

We discuss four off-shell N=4 D=1 supersymmetry transformations, their associated one-dimensional sigma-models and their mutual relations. They are given by I) the (4,4)_{lin} linear supermultiplet (supersymmetric extension of R^4), II) the (3,4,1)_{lin} linear supermultiplet (supersymmetric extension of R^3), III) the (3,4,1)_{nl} non-linear supermultiplet living on S^3 and IV) the (2,4,2)_{nl} non-linear supermultiplet living on S^2. The I -> II map is the supersymmetric extension of the R^4 -> R^3 bilinear map, while the II -> IV map is the supersymmetric extension of the S^3 -> S^2 first Hopf fibration. The restrictions on the S^3, S^2 spheres are expressed in terms of the stereographic projections. The non-linear supermultiplets, whose supertransformations are local differential polynomials, are not equivalent to the linear supermultiplets with the same field content. The sigma-models are determined in terms of an unconstrained prepotential of the target coordinates. The Uniformization Problem requires solving an inverse problem for the prepotential. The basic features of the supersymmetric extension of the second and third Hopf maps are briefly sketched. Finally, the Schur's lemma (i.e. the real, complex or quaternionic property) is extended to all minimal linear supermultiplets up to N<=8.Comment: 24 page

The geometry of N=4 twisted string

We compare N=2 string and N=4 topological string within the framework of the sigma model approach. Being classically equivalent on a flat background, the theories are shown to lead to different geometries when put in a curved space. In contrast to the well studied Kaehler geometry characterising the former case, in the latter case a manifold has to admit a covariantly constant holomorphic two-form in order to support an N=4 twisted supersymmetry. This restricts the holonomy group to be a subgroup of SU(1,1) and leads to a Ricci--flat manifold. We speculate that, the N=4 topological formalism is an appropriate framework to smooth down ultraviolet divergences intrinsic to the N=2 theory.Comment: 20 pages, LaTe

Hamiltonian reduction and supersymmetric mechanics with Dirac monopole

We apply the technique of Hamiltonian reduction for the construction of three-dimensional ${\cal N}=4$ supersymmetric mechanics specified by the presence of a Dirac monopole. For this purpose we take the conventional ${\cal N}=4$ supersymmetric mechanics on the four-dimensional conformally-flat spaces and perform its Hamiltonian reduction to three-dimensional system. We formulate the final system in the canonical coordinates, and present, in these terms, the explicit expressions of the Hamiltonian and supercharges. We show that, besides a magnetic monopole field, the resulting system is specified by the presence of a spin-orbit coupling term. A comparison with previous work is also carried out.Comment: 9 pages, LaTeX file, PACS numbers: 11.30.Pb, 03.65.-w, accepted for publication in PRD; minor changes in the Conclusion, the Bibliography and the Acknowledgemen

Applications of Graphene at Microwave Frequencies

In view to the epochal scenarios that nanotechnology discloses, nano-electronics has the potential to introduce a paradigm shift in electronic systems design similar to that of the transition from vacuum tubes to semiconductor devices. Since low dimensional (1D and 2D) nano-structured materials exhibit unprecedented electro-mechanical properties in a wide frequency range, including radio-frequencies (RF), microwave nano-electronics provides an enormous and yet widely undiscovered opportunity for the engineering community. Carbon nano-electronics is one of the main research routes of RF/microwave nano-electronics. In particular, graphene has shown proven results as an emblematic protagonist, and a real solution for a wide variety of microwave electronic devices and circuits. This paper introduces graphene properties in the microwave range, and presents a paradigm of novel graphene-based devices and applications in the microwave/RF frequency range

On the uniqueness of the unitary representations of the non commutative Heisenberg-Weyl algebra

In this paper we discuss the uniqueness of the unitary representations of the non commutative Heisenberg-Weyl algebra. We show that, apart from a critical line for the non commutative position and momentum parameters, the Stone-von Neumann theorem still holds, which implies uniqueness of the unitary representation of the Heisenberg-Weyl algebra.Comment: 4 page

Single Wall Nanotubes: Atomic Like Behaviour and Microscopic Approach

Recent experiments about the low temperature behaviour of a Single Wall Carbon Nanotube (SWCNT) showed typical Coulomb Blockade (CB) peaks in the zero bias conductance and allowed us to investigate the energy levels of interacting electrons. Other experiments confirmed the theoretical prediction about the crucial role which the long range nature of the Coulomb interaction plays in the correlated electronic transport through a SWCNT with two intramolecular tunneling barriers. In order to investigate the effects on low dimensional electron systems due to the range of electron electron repulsion, we introduce a model for the interaction which interpolates well between short and long range regimes. Our results could be compared with experimental data obtained in SWCNTs and with those obtained for an ideal vertical Quantum Dot (QD). For a better understanding of some experimental results we also discuss how defects and doping can break some symmetries of the bandstructure of a SWCNT.Comment: 8 pages, 4 figure

Complete Lagrangian formulation for N=4 topological string

We give a Lagrangian and display all local symmetries for N=4 topological string by Berkovits, Vafa and Siegel, the latter previously known in the superconformal gauge. Leading to a small N=4 superconformal algebra and exhibiting the manifest Lorentz invariance the model is proposed to be a framework for restoring the manifest Lorentz invariance in N=2 string scattering amplitudes.Comment: 8 pages, LaTex. One reference corrected, to appear in Phys. Rev.

On Quantum Special Kaehler Geometry

We compute the effective black hole potential V of the most general N=2, d=4 (local) special Kaehler geometry with quantum perturbative corrections, consistent with axion-shift Peccei-Quinn symmetry and with cubic leading order behavior. We determine the charge configurations supporting axion-free attractors, and explain the differences among various configurations in relations to the presence of ``flat'' directions of V at its critical points. Furthermore, we elucidate the role of the sectional curvature at the non-supersymmetric critical points of V, and compute the Riemann tensor (and related quantities), as well as the so-called E-tensor. The latter expresses the non-symmetricity of the considered quantum perturbative special Kaehler geometry.Comment: 1+43 pages; v2: typo corrected in the curvature of Jordan symmetric sequence at page 2

Non-Commutative Corrections to the MIC-Kepler Hamiltonian

Non-commutative corrections to the MIC-Kepler System (i.e. hydrogen atom in the presence of a magnetic monopole) are computed in Cartesian and parabolic coordinates. Despite the fact that there is no simple analytic expression for non-commutative perturbative corrections to the MIC-Kepler spectrum, there is a term that gives rise to the linear Stark effect which didn't exist in the standard hydrogen model.Comment: 5 page