Comments on `Existence of axially symmetric solutions in SU(2)-Yang Mills and related theories [hep-th/9907222]'

TL;DR

This paper challenges previous claims by Hannibal that axially symmetric solutions do not exist in SU(2) Einstein-Yang-Mills-dilaton theory, providing explicit asymptotic forms for solutions with winding number 2.

Contribution

It explicitly constructs the asymptotic form of non-abelian solutions with winding number 2, disproving prior non-existence claims.

Findings

Explicit asymptotic form for solutions with winding number 2

Disproof of previous non-existence claim

Existence of axially symmetric solutions in the theory

Abstract

In [hep-th/9907222] Hannibal claims to exclude the existence of particle-like static axially symmetric non-abelian solutions in SU(2) Einstein-Yang-Mills-dilaton theory. His argument is based on the asymptotic behaviour of such solutions. Here we disprove his claim by giving explicitly the asymptotic form of non-abelian solutions with winding number n=2.