Euclidean solutions of Yang-Mills theory coupled to a massive dilaton

TL;DR

This paper explores Euclidean Yang-Mills theory coupled with a massive dilaton, revealing infinite branches of regular, spherically symmetric solutions that serve as new saddle points in the Euclidean path integral.

Contribution

It demonstrates the existence of infinitely many regular solutions in the Euclidean Yang-Mills-dilaton system for any dilaton mass, classified by the number of gauge field nodes.

Findings

Infinite branches of solutions exist for all dilaton masses.

Solutions are labeled by the number of gauge field nodes.

These solutions have finite reduced action and are new saddle points.

Abstract

The Euclidean version of Yang-Mills theory coupled to a massive dilaton is investigated. Our analytical and numerical results imply existence of infinite number of branches of globally regular, spherically symmetric, dyonic type solutions for any values of dilaton mass $m$. Solutions on different branches are labelled by the number of nodes of gauge field amplitude $W$. They have finite reduced action and provide new saddle points in the Euclidean path integral.