  In this article, we study wormhole spacetimes in the framework of the static
spherically symmetric SU(2) Einstein-Yang-Mills theory coupled to a phantom
scalar field. We show rigorously the existence of an infinite sequence of
symmetric wormhole solutions, labelled by the number of zeros of the Yang-Mills
potential. These solutions have previously been discovered numerically.
Mathematically, the problem resembles the pure Einstein-Yang-Mills system for
black hole initial conditions, which was well-studied in the 90s. The main
difference in the present work is that the coupling to the phantom field adds a
non-trivial degree of complexity to the analysis. After proving the existence
of the symmetric wormhole solutions, we also present numerical evidence for the
existence of asymmetric ones.
