Dilatonic formulation for conducting cosmic string models

Abstract

It can be shown how the the introduction of a suitably defined dilatonic auxiliary field, Φ say, makes it possible for the non-linear Lagrangian for a generic elastic string model, of the kind appropriate for representing superconducting cosmic strings, to be converted into a standardised form as the sum of a kinetic term that is just homogeneously quadratic in the relevant scalar phase gradient (as in a simple linear model) together with a potential energy term, V say, that is specified as a generically non-linear function of Φ. The explicit form of this function is derived for various noteworthy examples, of which the most memorable is that of the transonic string model, as characterised by a given mass scale, m say, for which this potential energy density will be expressible in terms of the zero current limit value Φ0 of Φ by