Nonabelian Bosonic Currents in Cosmic Strings

TL;DR

This paper explores a nonabelian extension of the cosmic string model with SU(2) currents, revealing three distinct types of current-carrying solutions, including a novel genuinely nonabelian case dependent on Lorentz invariants.

Contribution

It introduces a nonabelian generalization of the cosmic string model with SU(2) currents and classifies the possible current-carrying solutions, including a new nonabelian case.

Findings

Current solutions include abelian, lightlike, and nonabelian types.

The nonabelian case depends on Lorentz invariant phase gradients.

The nonabelian solution cannot be simplified with cylindrical symmetry.

Abstract

A nonabelian generalization of the neutral Witten current-carrying string model is discussed in which the bosonic current-carrier belongs to a two dimensional representation of SU(2). We find that the current-carrying solutions can be of three different kinds: either the current spans a U(1) subgroup, and in which case one is left with an abelian current-carrying string, or the three currents are all lightlike, travelling in the same direction (only left or right movers). The third, genuinely nonabelian situation, cannot be handled within a cylindrically symmetric framework, but can be shown to depend on all possible string Lorentz invariant quantities that can be constructed out of the phase gradients.