Einstein-Yang-Mills theory with a massive dilaton and axion: String-inspired regular and black hole solutions

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 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.