Einstein-Yang-Mills wormholes haunted by a phantom field

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.