Einstein-Yang-Mills solitons: towards new degrees of freedom

TL;DR

This paper explores new non-spherical, non-static solitons in Einstein-Yang-Mills theory, developing a non-perturbative framework for stationary axisymmetric solutions and examining their potential existence.

Contribution

It introduces a non-perturbative formulation for stationary axisymmetric EYM solitons using a (2+1)+1 reduction scheme and derives a 2D action for static configurations.

Findings

Derived a 2D dilaton gravity model for spherically symmetric configurations

Constructed a Euclidean representation for stationary axisymmetric SU(2) EYM system

Discussed the potential existence of cylindrical EYM sphalerons

Abstract

A recent progress in obtaining non-spherical and non-static solitons in the four-dimensional Einstein--Yang--Mills (EYM) theory is discussed, and a non-perturbative formulation of the stationary axisymmetric problem is attempted. First a 2D dilaton gravity model is derived for the spherically symmetric time-dependent configurations. Then a similar Euclidean representation is constructed for the stationary axisymmetric non-circular SU(2) EYM system using the (2+1)+1 reduction scheme suggested by Maeda, Sasaki, Nakamura and Miyama. The crucial role in this reduction is played by the extra terms entering the reduced Yang--Mills and Kaluza--Klein two-forms similarly to Chern--Simons terms in the theories with higher rank antisymmetric tensor fields. We also derive a simple 2D action describing static axisymmetric magnetic EYM configurations and discuss a possibility of existence of cylindrical EYM sphalerons.