Cylindrically symmetric solitons in Einstein-Yang-Mills theory

TL;DR

This paper investigates cylindrically symmetric Einstein-Yang-Mills soliton solutions, revealing their asymptotic Kasner structure, bifurcation behavior, and the conditions under which they resemble straight or circular strings, including analytical and numerical results.

Contribution

It provides a detailed analysis of regular cylindrically symmetric EYM solutions, deriving sum rules, exploring bifurcation structures, and demonstrating the superposition of string-like configurations due to Yang-Mills self-interactions.

Findings

Regular solutions have Kasner asymptotics.

Solutions bifurcate into string-like configurations.

Self-interaction terms enable superposition of strings.

Abstract

Recently new Einstein-Yang-Mills (EYM) soliton solutions were presented which describe superconducting strings with Kasner asymptotic (hep-th/0610183). Here we study the static cylindrically symmetric SU(2) EYM system in more detail. The ansatz for the gauge field corresponds to superposition of the azimuthal $B_\phi$ and the longitudinal $B_z$ components of the color magnetic field. We derive sum rules relating data on the symmetry axis to asymptotic data and show that generic asymptotic structure of regular solutions is Kasner. Solutions starting with vacuum data on the axis generically are divergent. Regular solutions correspond to some bifurcation manifold in the space of parameters which has the low-energy limiting point corresponding to string solutions in flat space (with the divergent total energy) and the high-curvature point where gravity is crucial. Some analytical results are presented for the low energy limit, and numerical bifurcation curves are constructed in the gravitating case. Depending on the parameters, the solution looks like a straight string or a pair of straight and circular strings. The existence of such non-linear superposition of two strings becomes possible due to self-interaction terms in the Yang-Mills action which suppress contribution of the circular string near the polar axis.