No abstract

One-loop corrections to kink masses in a family of (1+1)-dimensional field theoretical models with two real scalar fields are computed. A generalized DHN formula applicable to potentials with and without reflection is obtained. It is shown how half-bound states arising in the spectrum of the second order fluctuation operator for one-component topological kinks and the vacuum play a central rôle in the computation of the kink Casimir energy. The issue of whether or not the kink degeneracy exhibited by this family of models at the classical level survives one-loop quantum fluctuations is addressed .

We use the generalized zeta function regularization method to compute the one-loop quantum correction to the masses of the TK1 and TK2 kinks in a deformation of the O(N ) linear sigma model on the real line.

A formula is derived that allows the computation of one-loop mass shifts for self-dual semilocal topological solitons. These extended objects, which in three spatial dimensions are called semi-local strings, arise in a generalized Abelian Higgs model with a doublet of complex Higgs fields. Having a mixture of global, SU (2), and local (gauge), U (1), symmetries, this weird system may seem bizarre, but it is in fact the bosonic sector of electro-weak theory when the weak mixing angle is π 2 . The procedure for computing the semi-classical mass shifts is based on canonical quantization and heat kernel/zeta function regularization methods.

Non-linear sigma models with scalar fields taking values on CP n complex manifolds are addressed. In the simplest n = 1 case, where the target manifold is the S 2 sphere, we describe the scalar fields by means of stereographic maps. In this case when the U(1) symmetry is gauged and Maxwell and mass terms are allowed, the model accommodates stable self-dual vortices of two kinds with different energies per unit length and where the Higgs field winds at the cores around the two opposite poles of the sphere. Allowing for dielectric functions in the magnetic field, similar and richer self-dual vortices of different species in the south and north charts can be found by slightly modifying the potential. Two different situations are envisaged: either the vacuum orbit lies on a parallel in the sphere, or one pole and the same parallel form the vacuum orbit. Besides the selfdual vortices of two species, there exist BPS domain walls in the second case. Replacing the Maxwell contribution of the gauge field to the action by the second Chern-Simons secondary class, only possible in (2 + 1)-dimensional Minkowski space-time, new BPS topological defects of two species appear. Namely, both BPS vortices and domain ribbons in the south and the north charts exist because the vacuum orbit consits of the two poles and one parallel. Formulation of the gauged CP 2 model in a reference chart shows a self-dual structure such that BPS semi-local vortices exist. The transition functions to the second or third charts break the U(1) × SU(2) semi-local symmetry, but there is still room for standard self-dual vortices of the second species. The same structures encompassing N complex scalar fields are easily generalized to gauged CP N models.