Saddle point solutions in Yang-Mills-dilaton theory

TL;DR

This paper investigates non-perturbative static solutions in Yang-Mills-dilaton theory, revealing a family of regular solutions with specific stability properties, analyzed through analytical, numerical, and Morse-theory methods.

Contribution

It identifies a new family of regular, purely magnetic solutions with zero magnetic charge and analyzes their stability using Morse theory.

Findings

Existence of a countable family of regular solutions

Solutions are saddle points with multiple unstable modes

Energy spectrum is bounded above by the unit magnetic charge monopole

Abstract

The coupling of a dilaton to the $SU(2)$-Yang-Mills field leads to interesting non-perturbative static spherically symmetric solutions which are studied by mixed analitical and numerical methods. In the abelian sector of the theory there are finite-energy magnetic and electric monopole solutions which saturate the Bogomol'nyi bound. In the nonabelian sector there exist a countable family of globally regular solutions which are purely magnetic but have zero Yang-Mills magnetic charge. Their discrete spectrum of energies is bounded from above by the energy of the abelian magnetic monopole with unit magnetic charge. The stability analysis demonstrates that the solutions are saddle points of the energy functional with increasing number of unstable modes. The existence and instability of these solutions are "explained" by the Morse-theory argument recently proposed by Sudarsky and Wald.