177 research outputs found
On the solitons of the Chern-Simons-Higgs model
Several issues concerning the self-dual solutions of the Chern-Simons-Higgs
model are addressed. The topology of the configuration space of the model is
analysed when the space manifold is either the plane or an infinite cylinder.
We study the local structure of the moduli space of self-dual solitons in the
second case by means of an index computation. It is shown how to manage the
non-integer contribution to the heat-kernel supertrace due to the
non-compactness of the base space. A physical picture of the local coordinates
parametrizing the non-topological soliton moduli space arises .Comment: 27 pages, 3 figures, to appear in The European Physical Journal
One-dimensional solitary waves in singular deformations of SO(2) invariant two-component scalar field theory models
In this paper we study the structure of the manifold of solitary waves in
some deformations of SO(2) symmetric two-component scalar field theoretical
models in two-dimensional Minkowski space. The deformation is chosen in order
to make the analogous mechanical system Hamilton-Jacobi separable in polar
coordinates and displays a singularity at the origin of the internal plane. The
existence of the singularity confers interesting and intriguing properties to
the solitary waves or kink solutions.Comment: 25 pages, 18 figure
Perfectly invisible -symmetric zero-gap systems, conformal field theoretical kinks, and exotic nonlinear supersymmetry
We investigate a special class of the -symmetric quantum models
being perfectly invisible zero-gap systems with a unique bound state at the
very edge of continuous spectrum of scattering states. The family includes the
-regularized two particle Calogero systems (conformal quantum
mechanics models of de Alfaro-Fubini-Furlan) and their rational extensions
whose potentials satisfy equations of the KdV hierarchy and exhibit,
particularly, a behaviour typical for extreme waves. We show that the two
simplest Hamiltonians from the Calogero subfamily determine the fluctuation
spectra around the -regularized kinks arising as traveling waves
in the field-theoretical Liouville and conformal Toda systems. Peculiar
properties of the quantum systems are reflected in the associated exotic
nonlinear supersymmetry in the unbroken or partially broken phases. The
conventional supersymmetry is extended here to the
nonlinear supersymmetry that involves two bosonic generators
composed from Lax-Novikov integrals of the subsystems, one of which is the
central charge of the superalgebra. Jordan states are shown to play an
essential role in the construction.Comment: 33 pages; comments and refs added, version to appear in JHE
On a family of (1+1)-dimensional scalar field theory models: kinks, stability, one-loop mass shifts
In this paper we construct a one-parametric family of (1+1)-dimensional
one-component scalar field theory models supporting kinks. Inspired by the
sine-Gordon and models, we look at all possible extensions such that
the kink second-order fluctuation operators are Schr\"odinger differential
operators with P\"oschl-Teller potential wells. In this situation, the
associated spectral problem is solvable and therefore we shall succeed in
analyzing the kink stability completely and in computing the one-loop quantum
correction to the kink mass exactly. When the parameter is a natural number,
the family becomes the hierarchy for which the potential wells are
reflectionless, the two first levels of the hierarchy being the sine-Gordon and
models.Comment: 23 pages, 4 figures, to be published in Annals of Physic
Self-Dual Vortices in Abelian Higgs Models with Dielectric Function on the Noncommutative Plane
We show that Abelian Higgs Models with dielectric function defined on the
noncommutative plane enjoy self-dual vorticial solutions. By choosing a
particular form of the dielectric function, we provide a family of solutions
whose Higgs and magnetic fields interpolate between the profiles of the
noncommutative Nielsen-Olesen and Chern-Simons vortices. This is done both for
the usual model and for the semilocal model with a
doublet of complex scalar fields. The variety of known noncommutative self-dual
vortices which display a regular behaviour when the noncommutativity parameter
tends to zero results in this way considerably enlarged
Quantum-induced interactions in the moduli space of degenerate BPS domain walls
In this paper quantum effects are investigated in a very special two-scalar
field model having a moduli space of BPS topological defects. In a
-dimensional space-time the defects are classically degenerate in mass
kinks, but in dimensions the kinks become BPS domain walls, all of them
sharing the same surface tension at the classical level. The heat kernel/zeta
function regularization method will be used to control the divergences induced
by the quantum kink and domain wall fluctuations. A generalization of the
Gilkey-DeWitt-Avramidi heat kernel expansion will be developed in order to
accommodate the infrared divergences due to zero modes in the spectra of the
second-order kink and domain wall fluctuation operators, which are respectively
matrix ordinary or partial differential operators. Use of these
tools in the spectral zeta function associated with the Hessian operators paves
the way to obtain general formulas for the one-loop kink mass and domain wall
tension shifts in any - or -dimensional -component scalar
field theory model. Application of these formulae to the BPS kinks or domain
walls of the model mentioned above reveals the breaking of the classical
mass or surface tension degeneracy at the quantum level. Because the main
parameter distinguishing each member in the BPS kink or domain wall moduli
space is essentially the distance between the centers of two basic kinks or
walls, the breaking of the degeneracy amounts to the surge in quantum-induced
forces between the two constituent topological defects. The differences in
surface tension induced by one-loop fluctuations of BPS walls give rise mainly
to attractive forces between the constituent walls except if the two basic
walls are very far apart. Repulsive forces between two close walls only arise
if the coupling is approaches the critical value from below.Comment: 34 pages, 7 figures, to appear in JHE
Higgs phase in a gauge non-linear -model. Two species of BPS vortices and their zero modes
In this paper zero modes of fluctuation are dissected around the two species
of BPS vortices existing in the critical Higgs phase, where the scalar and
vector meson masses are equal, of a gauged nonlinear
-model. If , , is the quantized
magnetic flux of the two species of BPS vortex solutions, linearly
independent vortex zero modes for each species are found and described. The
existence of two species of moduli spaces of dimension of these stringy
topological defects is thus locally shown.Comment: 17 pages, 28 figure
generalized Robin boundary conditions and quantum vacuum fluctuations
The effects induced by the quantum vacuum fluctuations of one massless real
scalar field on a configuration of two partially transparent plates are
investigated. The physical properties of the infinitely thin plates are
simulated by means of Dirac- point interactions. It is
shown that the distortion caused on the fluctuations by this external
background gives rise to a generalization of Robin boundary conditions. The
-operator for potentials concentrated on points with non defined parity is
computed with total generality. The quantum vacuum interaction energy between
the two plates is computed using the formula to find positive, negative,
and zero Casimir energies. The parity properties of the
potential allow repulsive quantum vacuum force between identical plates.Comment: 21 pages and 11 figures. PhysRev
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