Domain walls in a generalized Chern–Simons model

We consider global topological defects in symmetry breaking models with a non-canonical kinetic term. Apart from a mass parameter entering the potential, one additional dimensional parameter arises in such models -- a ``kinetic'' mass. The properties of defects in these models are quite different from ``standard'' global domain walls, vortices and monopoles, if their kinetic mass scale is smaller than their symmetry breaking scale. In particular, depending on the concrete form of the kinetic term, the typical size of such a defect can be either much larger or much smaller than the size of a standard defect with the same potential term. The characteristic mass of a non-standard defect, which might have been formed during a phase transition in the early universe, depends on both the temperature of a phase transition and the kinetic mass.

We investigate the presence of defects in systems described by real scalar field in (D,1) spacetime dimensions. We show that when the potential assumes specific form, there are models which support stable global defects for D arbitrary. We also show how to find first-order differential equations that solve the equations of motion, and how to solve models in D dimensions via soluble problems in D=1. We illustrate the procedure examining specific models and finding explicit solutions.

We consider gauge vortices in symmetry breaking models with a non-canonical kinetic term. This work extends our previous study on global topological k-defects (hep-th/0608071), including a gauge field. The model consists of a scalar field with a non-canonical kinetic term, while for the gauge field the standard form of its kinetic term is preserved. Topological defects arising in such models, k-vortices, may have quite different properties as compared to ``standard'' vortices. This happens because an additional dimensional parameter enters the Lagrangian for the considered model -- a ``kinetic'' mass. We briefly discuss possible consequences for cosmology, in particular, the formation of cosmic strings during phase transitions in the early universe and their properties.