Gravitating Meron-like topological solitons in massive Yang–Mills theory and the Einstein–Skyrme model

We show that Merons in D-dimensional Einstein–Massive–Yang–Mills theory can be mapped to solutions of the Einstein–Skyrme model. The identification of the solutions relies on the fact that, when considering the Meron ansatz for the gauge connection $$A=\lambda U^{-1}dU$$ A = λ U - 1 d U , the massive Yang–Mills equations reduce to the Skyrme equations for the corresponding group element U. In the same way, the energy–momentum tensors of both theories can be identified and therefore lead to the same Einstein equations. Subsequently, we focus on the SU(2) case and show that introducing a mass for the Yang–Mills field restricts Merons to live on geometries given by the direct product of $$S^3$$ S 3 (or $$S^2$$ S 2 ) and Lorentzian manifolds with constant Ricci scalar. We construct explicit examples for $$D=4$$ D = 4 and $$D=5$$ D = 5 . Finally, we comment on possible generalisations.