J. Sanchez-Guillen

K fields, compactons and thick branes

K fields, that is, fields with a non-standard kinetic term, allow for soliton solutions with compact support, i.e., compactons. Compactons in 1+1 dimensions may give rise to topological defects of the domain wall type and with finite thickness in higher dimensions. Here we demonstrate that, for an appropriately chosen kinetic term, propagation of linear perturbations is completely suppressed outside the topological defect, confining the propagation of particles inside the domain wall. On the other hand, inside the topological defect the propagation of linear perturbations is of the standard type, in spite of the non-standard kinetic term. Consequently, this compacton domain wall may act like a brane of finite thickness which is embedded in a higher dimensional space, but to which matter fields are constrained. In addition, we find strong indications that, when gravity is taken into account, location of gravity in the sense of Randall--Sundrum works for these compacton domain walls. When seen from the bulk, these finite thickness branes, in fact, cannot be distinguished from infinitely thin branes.

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 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.

Extended supersymmetry and BPS solutions in baby Skyrme models

A bstractWe 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.

N=1 supersymmetric extension of the baby Skyrme model

We construct a method to supersymmetrize higher kinetic terms and apply it to the baby Skyrme model. We find that there exist N=1 supersymmetric extensions for baby Skyrme models with arbitrary potential.

Investigation of restricted baby Skyrme models

A restriction of the baby Skyrme model consisting of the quartic and potential terms only is investigated in detail for a wide range of potentials. Further, its properties are compared with those of the corresponding full baby Skyrme models. We find that topological (charge) as well as geometrical (nucleus/shell shape) features of baby Skyrmions are captured already by the soliton solutions of the restricted model. Further, we find a coincidence between the compact or noncompact nature of solitons in the restricted model, on the one hand, and the existence or nonexistence of multi-Skyrmions in the full baby Skyrme model, on the other hand.

Compact gauge K vortices

We investigate a version of the Abelian Higgs model with a non-standard kinetic term (K-field theory) in (2+1) dimensions. The existence of vortex-type solutions with compact support (topological compactons) is established by a combination of analytical and numerical methods. This result demonstrates that the concept of compact solitons in K-field theories can be extended to higher dimensions.

Compact self-gravitating solutions of quartic (K) fields in brane cosmology

Recently we proposed that K fields, that is, fields with a non-standard kinetic term, may provide a mechanism for the generation of thick branes, based on the following observations. First, K field theories allow for soliton solutions with compact support, i.e., compactons. Compactons in 1+1 dimensions may give rise to topological defects of the domain wall type and with finite thickness in higher dimensions. Second, propagation of linear perturbations is confined inside the compacton domain wall. Further, these linear perturbations inside the topological defect are of the standard type, in spite of the non-standard kinetic term. Third, when gravity is taken into account, location of gravity in the sense of Randall–Sundrum works for these compacton domain walls provided that the backreaction of gravity does not destabilize the compacton domain wall. It is the purpose of the present paper to investigate in detail the existence and stability of compacton domain walls in the full K field and gravity system, using both analytical and numerical methods. We find that the existence of the domain wall in the full system requires a correlation between the gravitational constant and the bulk cosmological constant.

BPS Skyrmions as neutron stars

The BPS Skyrme model has been demonstrated already to provide a physically intriguing and quantitatively reliable description of nuclear matter. Indeed, the model has both the symmetries and the energy–momentum tensor of a perfect fluid, and thus represents a field theoretic realization of the “liquid droplet” model of nuclear matter. In addition, the classical soliton solutions together with some obvious corrections (spin–isospin quantization, Coulomb energy, proton–neutron mass difference) provide an accurate modeling of nuclear binding energies for heavier nuclei. These results lead to the rather natural proposal to try to describe also neutron stars by the BPS Skyrme model coupled to gravity. We find that the resulting self-gravitating BPS Skyrmions provide excellent results as well as some new perspectives for the description of bulk properties of neutron stars when the parameter values of the model are extracted from nuclear physics. Specifically, the maximum possible mass of a neutron star before black-hole formation sets in is a few solar masses, the precise value of which depends on the precise values of the model parameters, and the resulting neutron star radius is of the order of 10 km.

Investigation of the Nicole model

We study soliton solutions of the Nicole model—a non-linear four-dimensional field theory consisting of the CP1 Lagrangian density to the non-integer power 32—using an ansatz within toroidal coordinates, which is indicated by the conformal symmetry of the static equations of motion. We calculate the soliton energies numerically and find that they grow linearly with the topological charge (Hopf index). Further we prove this behavior to hold exactly for the ansatz. On the other hand, for the full three-dimensional system without symmetry reduction we prove a sub-linear upper bound, analogously to the case of the Faddeev–Niemi model. It follows that symmetric solitons cannot be true minimizers of the energy for sufficiently large Hopf index, again in analogy to the Faddeev–Niemi model.

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.