Einstein-Yang-Mills Theory with a Massive Dilaton and Axion: String-Inspired Regular and Black Hole Solutions

TL;DR

This paper explores string-inspired Einstein-Yang-Mills theories with massive dilaton and axion fields, presenting new regular and black hole solutions under static, spherically symmetric conditions, and analyzing their physical properties.

Contribution

It introduces and numerically constructs novel regular and black hole solutions in a string-inspired Einstein-Yang-Mills framework with massive dilaton and axion fields.

Findings

Numerical regular solutions for the dilaton-coupled Yang-Mills system.

Black hole solutions with nontrivial dilaton profiles.

Analysis of dyonic configurations with rapid decay of electric and magnetic fields.

Abstract

We study the classical theory of a non-Abelian gauge field (gauge group $SU(2)$) coupled to a massive dilaton, massive axion and Einstein gravity. The theory is inspired by the bosonic part of the low-energy heterotic string action for a general Yang-Mills field, which we consider to leading order after compactification to $(3+1)$ dimensions. We impose the condition that spacetime be static and spherically symmetric, and we introduce masses via a dilaton-axion potential associated with supersymmetry (SUSY)-breaking by gaugino condensation in the hidden sector. In the course of describing the possible non-Abelian solutions of the simplified theory, we consider in detail two candidates: a massive dilaton coupled to a purely magnetic Yang-Mills field, and a massive axion field coupled to a non-Abelian dyonic configuration, in which the electric and magnetic fields decay too rapidly to correspond to any global gauge charge. We discuss the feasibility of solutions with and without a nontrivial dilaton for the latter case, and present numerical regular and black hole solutions for the former.