Dilatonic formulation for conducting cosmic string models

Abstract

It is 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 $Φ_{_0}$ of $Φ$ by $ V= {1\over 2} m \big(Φ_{_0}^{-2} Φ^2+ Φ_{_0}^{2} Φ^{-2} \big)$.