On the regularity of static axially symmetric solutions in SU(2) Yang-Mills-dilaton theory

TL;DR

This paper demonstrates that static axially symmetric solutions in SU(2) Yang-Mills-dilaton theory, previously considered singular, can be gauge transformed into regular solutions, clarifying their mathematical structure.

Contribution

It shows that solutions obtained with a singular Ansatz are gauge equivalent to regular solutions, providing explicit gauge transformations at key points.

Findings

Singular solutions are gauge equivalent to regular ones.

Explicit gauge transformations are provided at the axis and origin.

Regularity of solutions is established through gauge transformations.

Abstract

The regularity of static axially symmetric solutions in SU(2) Yang-Mills-dilaton theory is examined. We show that the solutions obtained previously within a singular Ansatz for the non-abelian gauge field can be gauge transformed into a regular form. The local form of the gauge transformation is given on the singular axis and at the origin.