Axially Symmetric Multisphalerons in Yang-Mills-Dilaton Theory

TL;DR

This paper constructs axially symmetric multisphaleron solutions in SU(2) Yang-Mills-dilaton theory, generalizing known spherically symmetric solutions and revealing their relation to abelian magnetic monopoles with quantized charge.

Contribution

It introduces new sequences of multisphaleron solutions with axial symmetry and explores their properties and limits, extending previous spherically symmetric results.

Findings

Sequences labeled by winding number n>1 are constructed.

Solutions reduce to abelian magnetic monopoles with n units of charge.

Energy scales proportionally with the charge n.

Abstract

We construct sequences of axially symmetric multisphaleron solutions in SU(2) Yang-Mills-dilaton theory. The sequences are labelled by a winding number $n>1$. For $n=1$ the known sequence of spherically symmetric sphaleron solutions is obtained. The solutions within each sequence are labelled by the number of nodes $k$ of the gauge field functions. The limiting solutions of the sequences correspond to abelian magnetic monopoles with $n$ units of charge and energy $E \propto n$.