1,823 research outputs found
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
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
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.
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
Noncommutative Coulombic Monopole
We have constructed the appropriate Hamiltonian of the noncommutative
coulombic monopole (i.e. the noncommutative hydrogen atom with a monopole). The
energy levels of this system have been calculated, discussed and compared with
the noncommutative hydrogen atom ones. The main emphasis is put on the ground
state. In addition, the Stark effect for the noncommutative coulombic monopole
has been studied.Comment: 5 pages, PACS numbers: 03.65.-w, 14.80.Hv, 02.40.Gh, 32.60.+
Coherent Bremsstrahlung in Imperfect Periodic Atomic Structures
Coherent bremsstrahlung of high energy electrons moving in a
three-dimensional imperfect periodic lattice consisting of a complicated system
of atoms is considered. On the basis of the normalized probability density
function of the distribution of atomic centers in the fundamental cell the
relations describing coherent and incoherent contributions into cross sections
are obtained. In particular, the cross section of coherent bremsstrahlung in
complex polyatomic single crystals is found.
The peculiarities of formation and possibilities of utilization of coherent
processes are discussed.Comment: 23 pages, 8 figures, to be published in Phys. Rev.
A note on N=4 supersymmetric mechanics on K\"ahler manifolds
The geometric models of N=4 supersymmetric mechanics with
(2d.2d)_{\DC}-dimensional phase space are proposed, which can be viewed as
one-dimensional counterparts of two-dimensional N=2 supersymmetric sigma-models
by Alvarez-Gaum\'e and Freedman. The related construction of supersymmetric
mechanics whose phase space is a K\"ahler supermanifold is considered. Also,
its relation with antisymplectic geometry is discussed.Comment: 4 pages, revte
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