Fermions in the Background of Dilatonic Sphalerons

TL;DR

This paper investigates a sequence of static solutions in Yang-Mills-dilaton theory, revealing fermion zero modes and analyzing their stability, with odd solutions exhibiting sphaleron-like properties.

Contribution

It introduces and analyzes a discrete sequence of solutions with fermion zero modes, highlighting their sphaleron characteristics and stability properties.

Findings

Solutions with odd n have sphaleron properties.

Normalizable fermion zero modes exist in these backgrounds.

The stability of solutions is critically examined.

Abstract

We discuss the properties and interpretation of a discrete sequence of a static spherically symmetric solutions of the Yang-Mills-dilaton theory. This sequence is parametrized by the number $n$ of zeros of a component of the gauge field potential. It is demonstrated that solutions with odd $n$ posses all the properties of the sphaleron. It is shown that there are normalizable fermion zero modes in the background of these solutions. The question of instability is critically analysed.