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 \(A=\lambda U^{-1}dU\), 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 \(S^3\) (or \(S^2\)) and Lorentzian manifolds with constant Ricci scalar. We construct explicit examples for \(D=4\) and \(D=5\). Finally, we comment on possible generalisations.

我们表明，D维爱因斯坦-大质量-杨-米尔斯理论中的梅隆可以映射到爱因斯坦-斯凯尔姆模型的解。解的识别依赖于这样一个事实：当考虑规范连接\(A=\lambda U^{-1}dU\)的 Meron ansatz 时，大规模的 Yang-Mills 方程简化为相应的 Skyrme 方程组元素U。以同样的方式，可以确定两种理论的能量-动量张量，从而得出相同的爱因斯坦方程。随后，我们专注于SU (2) 情况，并表明为 Yang-Mills 场引入质量会限制 Merons 生活在由\(S^3\)（或\(S^2\ )) 和具有常数 Ricci 标量的洛伦兹流形。我们为\(D=4\)和\(D=5\)构造显式示例。最后，我们评论可能的概括。