k-defects as compactons

We argue that topological compactons (solitons with compact support) may be quite common objects if $k$-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 $\phi^4$ 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 $B_\mu$ and the vector meson field $\omega_\mu$. 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.