Static, spherically symmetric solutions of Yang-Mills-Dilaton theory

TL;DR

This paper classifies static, spherically symmetric solutions in Yang-Mills-Dilaton theory into three classes—singular, regular, and oscillating—providing asymptotic formulas and numerical validation for these solutions.

Contribution

It systematically analyzes the solution space of Yang-Mills-Dilaton equations, identifying distinct classes and deriving asymptotic behaviors for regular solutions.

Findings

Regular solutions are characterized by the number of nodes in the Yang-Mills potential.

Existence of a discrete set of globally regular solutions confirmed.

Asymptotic formulas for parameters of regular solutions are derived and validated numerically.

Abstract

Static, spherically symmetric solutions of the Yang-Mills-Dilaton theory are studied. It is shown that these solutions fall into three different classes. The generic solutions are singular. Besides there is a discrete set of globally regular solutions further distinguished by the number of nodes of their Yang-Mills potential. The third class consists of oscillating solutions playing the role of limits of regular solutions, when the number of nodes tends to infinity. We show that all three sets of solutions are non-empty. Furthermore we give asymptotic formulae for the parameters of regular solutions and confront them with numerical results.