130 research outputs found
k-defects as compactons
We argue that topological compactons (solitons with compact support) may be
quite common objects if -fields, i.e., fields with nonstandard kinetic term,
are considered, by showing that even for models with well-behaved potentials
the unusual kinetic part may lead to a power-like approach to the vacuum, which
is a typical signal for the existence of compactons. The related approximate
scaling symmetry as well as the existence of self-similar solutions are also
discussed. As an example, we discuss domain walls in a potential Skyrme model
with an additional quartic term, which is just the standard quadratic term to
the power two. We show that in the critical case, when the quadratic term is
neglected, we get the so-called quartic model, and the corresponding
topological defect becomes a compacton. Similarly, the quartic sine-Gordon
compacton is also derived. Finally, we establish the existence of topological
half-compactons and study their properties.Comment: the stability proof of Section 4.4 corrected, some references adde
BPS submodels of the Skyrme model
We show that the standard Skyrme model without pion mass term can be
expressed as a sum of two BPS submodels, i.e., of two models whose static field
equations, independently, can be reduced to first order equations. Further,
these first order (BPS) equations have nontrivial solutions, at least locally.
These two submodels, however, cannot have common solutions. Our findings also
shed some light on the rational map approximation. Finally, we consider certain
generalisations of the BPS submodels.Comment: Latex, 12 page
Integrability from an abelian subgroup of the diffeomorphism group
It has been known for some time that for a large class of non-linear field
theories in Minkowski space with two-dimensional target space the complex
eikonal equation defines integrable submodels with infinitely many conservation
laws. These conservation laws are related to the area-preserving
diffeomorphisms on target space. Here we demonstrate that for all these
theories there exists, in fact, a weaker integrability condition which again
defines submodels with infinitely many conservation laws. These conservation
laws will be related to an abelian subgroup of the group of area-preserving
diffeomorphisms. As this weaker integrability condition is much easier to
fulfil, it should be useful in the study of those non-linear field theories.Comment: 13 pages, Latex fil
Extended Supersymmetry and BPS solutions in baby Skyrme models
We continue the investigation of supersymmetric extensions of baby Skyrme
models in d=2+1 dimensions. In a first step, we show that the CP(1) form of the
baby Skyrme model allows for the same N=1 SUSY extension as its O(3)
formulation. Then we construct the N=1 SUSY extension of the gauged baby Skyrme
model, i.e., the baby Skyrme model coupled to Maxwell electrodynamics. In a
next step, we investigate the issue of N=2 SUSY extensions of baby Skyrme
models. We find that all gauged and ungauged submodels of the baby Skyrme model
which support BPS soliton solutions allow for an N=2 extension such that the
BPS solutions are one-half BPS states (i.e., annihilated by one-half of the
SUSY charges). In the course of our investigation, we also derive the general
BPS equations for completely general N=2 supersymmetric field theories of (both
gauged and ungauged) chiral superfields, and apply them to the gauged nonlinear
sigma model as a further, concrete example.Comment: 32 pages, Latex fil
Supersymmetric extensions of K field theories
We review the recently developed supersymmetric extensions of field theories
with non-standard kinetic terms (so-called K field theories) in two an three
dimensions. Further, we study the issue of topological defect formation in
these supersymmetric theories. Specifically, we find supersymmetric K field
theories which support topological kinks in 1+1 dimensions as well as
supersymmetric extensions of the baby Skyrme model for arbitrary nonnegative
potentials in 2+1 dimensions.Comment: Contribution to the Proceedings of QTS7, Prague, August 201
Some Comments on BPS systems
We look at simple BPS systems involving more than one field. We discuss the
conditions that have to be imposed on various terms in Lagrangians involving
many fields to produce BPS systems and then look in more detail at the simplest
of such cases. We analyse in detail BPS systems involving 2 interacting
Sine-Gordon like fields, both when one of them has a kink solution and the
second one either a kink or an antikink solution. We take their solitonic
static solutions and use them as initial conditions for their evolution in
Lorentz covariant versions of such models. We send these structures towards
themselves and find that when they interact weakly they can pass through each
other with a phase shift which is related to the strength of their interaction.
When they interact strongly they repel and reflect on each other. We use the
method of a modified gradient flow in order to visualize the solutions in the
space of fields.Comment: 27 pages, 17 figure
The vector BPS baby Skyrme model
We investigate the relation between the BPS baby Skyrme model and its vector
meson formulation, where the baby Skyrme term is replaced by a coupling between
the topological current and the vector meson field . The
vector model still possesses infinitely many symmetries leading to infinitely
many conserved currents which stand behind its solvability. It turns out that
the similarities and differences of the two models depend strongly on the
specific form of the potential. We find, for instance, that compactons (which
exist in the BPS baby Skyrme model) disappear from the spectrum of solutions of
the vector counterpart. Specifically, for the vector model with the old baby
Skyrme potential we find that it has compacton solutions only provided that a
delta function source term effectively screening the topological charge is
inserted at the compacton boundary. For the old baby Skyrme potential squared
we find that the vector model supports exponentially localized solitons, like
the BPS baby Skyrme model. These solitons, however, saturate a BPS bound which
is a nonlinear function of the topological charge and, as a consequence, higher
solitons are unstable w.r.t. decay into smaller ones, which is at variance with
the more conventional situation (a linear BPS bound and stable solitons) in the
BPS baby Skyrme model.Comment: 20 pages, 4 figure
Thermodynamics of the BPS Skyrme model
One problem in the application of the Skyrme model to nuclear physics is that
it predicts too large a value for the compression modulus of nuclear matter.
Here we investigate the thermodynamics of the BPS Skyrme model at zero
temperature and calculate its equation of state. Among other results, we find
that classically (i.e. without taking into account quantum corrections) the
compressibility of BPS skyrmions is, in fact, infinite, corresponding to a zero
compression modulus. This suggests that the inclusion of the BPS submodel into
the Skyrme model lagrangian may significantly reduce this too large value,
providing further evidence for the claim that the BPS Skyrme model may play an
important role in the description of nuclei and nuclear matter.Comment: Latex, 26 pages, 1 figure; v2: some typos corrected, version accepted
for publication in Phys. Rev.
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