论文标题
在大规模阳米尔斯理论和爱因斯坦 - 凯尔姆模型中引诱梅隆样拓扑孤子
Gravitating Meron-like topological solitons in massive Yang-Mills theory and the Einstein-Skyrme model
论文作者
论文摘要
我们表明，在$ d $ d $维的大规模阳米尔斯理论中引诱的梅隆可以映射到爱因斯坦 - 锡基尔姆模型的解决方案。解决方案的识别依赖于以下事实：当考虑仪表连接的Meron Ansatz $ a =λu^{ - 1} du $时，大量的Yang-mills方程将相应的组元素$ u $降低到Skyrme方程。以同样的方式，可以识别这两种理论的能量量张量，因此导致相同的爱因斯坦方程。随后，我们专注于$ su（2）$ case，并表明为Yang-Mills Field的质量限制了Merons的质量，以$ s^3 $（或$ S^2 $）和Lorentzian歧管的直接乘积和持续的Ricci Scalar的直接乘积为生。我们为$ d = 4 $和$ d = 5 $构建明确的示例。最后，我们评论可能的概括。
We show that gravitating Merons in $D$-dimensional 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 $A=λU^{-1}dU$, 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.
