八维空间中的交替自对偶引力
Alternative Self-dual Gravity in Eight Dimensions
摘要：
我们开发了一个替代Ashtekar形式主义在八个维度。事实上，使用麦克道尔-曼尼托物理框架和自对偶曲率对称性，我们提出了一个行动，在八个维度中，Levi-Civita男高音与八个指数起着关键作用。我们明确地表明，这样的行动包含的数量的线性，二次和三次的黎曼张量，Ricci张量和标量曲率。特别地，线性项在八维空间中被简化为具有宇宙学常数的爱因斯坦-希尔伯特作用量。我们证明了这样一个约化作用量等价于八维空间中的Lovelock作用量。
英文摘要：
We develop an alternative Ashtekar formalism in eight dimensions. In fact, using a MacDowell-Mansouri physical framework and a self-dual curvature symmetry we propose an action in eight dimensions in which the Levi-Civita tenor with eight indices plays a key role. We explicitly show that such an action contains number of linear, quadratic and cubic terms in the Riemann tensor, Ricci tensor and scalar curvature. In particular, the linear term is reduced to the Einstein-Hilbert action with cosmological constant in eight dimensions. We prove that such a reduced action is equivalent to the Lovelock action in eight dimensions.
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