New results on twinlike models

In this work we study the presence of kinks in models described by a single real scalar field in bidimensional spacetime. We work within the first-order framework, and we show how to write first-order differential equations that solve the equations of motion. The first-order equations strongly simplify the study of linear stability, which is implemented on general grounds. They also lead to a direct investigation of twinlike theories, which is used to introduce a family of models that support the same defect structure, with the very same energy density and linear stability.Comment: 6 pages, 1 figur

Light Nuclei as Quantized Skyrmions

We consider the rigid body quantization of Skyrmions with topological charges 1 to 8, as approximated by the rational map ansatz. Novel, general expressions for the elements of the inertia tensors, in terms of the approximating rational map, are presented and are used to determine the kinetic energy contribution to the total energy of the ground and excited states of the quantized Skyrmions. Our results are compared to the experimentally determined energy levels of the corresponding nuclei, and the energies and spins of a few as yet unobserved states are predicted.Comment: 33 pages, 16 figures, Section 13 replace

Reparametrising the Skyrme Model using the Lithium-6 Nucleus

The minimal energy B=6 solution of the Skyrme model is a static soliton with $D_{4d}$ symmetry. The symmetries of the solution imply that the quantum numbers of the ground state are the same as those of the Lithium-6 nucleus. This identification is considered further by obtaining expressions for the mean charge radius and quadrupole moment, dependent only on the Skyrme model parameters $e$ (a dimensionless constant) and $F_\pi$ (the pion decay constant). The optimal values of these parameters have often been deliberated upon, and we propose, for $B>2$, changing them from those which are most commonly accepted. We obtain specific values for these parameters for B=6, by matching with properties of the Lithium-6 nucleus. We find further support for the new values by reconsidering the $\alpha$-particle and deuteron as quantized B=4 and B=2 Skyrmions.Comment: 18 page

Zero Modes of Rotationally Symmetric Generalized Vortices and Vortex Scattering

Zero modes of rotationally symmetric vortices in a hierarchy of generalized Abelian Higgs models are studied. Under the finite-energy and the smoothness condition, it is shown, that in all models, $n$ self-dual vortices superimposed at the origin have $2n$ modes. The relevance of these modes for vortex scattering is discussed, first in the context of the slow-motion approximation. Then a corresponding Cauchy problem for an all head-on collision of $n$ vortices is formulated. It is shown that the solution of this Cauchy problem has a $\frac{\pi}{n}$ symmetry.Comment: 12 pages. late

Gauged vortices in a background

We discuss the statistical mechanics of a gas of gauged vortices in the canonical formalism. At critical self-coupling, and for low temperatures, it has been argued that the configuration space for vortex dynamics in each topological class of the abelian Higgs model approximately truncates to a finite-dimensional moduli space with a Kaehler structure. For the case where the vortices live on a 2-sphere, we explain how localisation formulas on the moduli spaces can be used to compute explicitly the partition function of the vortex gas interacting with a background potential. The coefficients of this analytic function provide geometrical data about the Kaehler structures, the simplest of which being their symplectic volume (computed previously by Manton using an alternative argument). We use the partition function to deduce simple results on the thermodynamics of the vortex system; in particular, the average height on the sphere is computed and provides an interesting effective picture of the ground state.Comment: Final version: 22 pages, LaTeX, 1 eps figur