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arXiv 1406.3291hep-thgr-qc
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de Sitter空间中的反足对称规范场和高自旋引力

Antipodally symmetric gauge fields and higher-spin gravity in de Sitter space

Yasha Neiman

摘要:

研究了de Sitter空间中任意自旋的规范场。这些包括杨-米尔斯场和引力子,以及瓦西里耶夫理论中的高自旋场。我们专注于反对足对称的解决方案的场方程,即生活在“椭圆”德西特空间dS_4/Z_2。对于自由领域,我们发现这样的解决方案,包括边界到散装传播的跨度集。我们发现dS_4/Z_2上的自由解在无穷远处只能有两种边界数据中的一种,即边界2点函数为零。在Vasiliev理论中,这种性质在相互作用中逐阶保持,即dS_4/Z_2中的边界n点函数都为零。这意味着基于洛伦兹dS_4/Z_2作用量的高自旋dS/CFT是空的。对于更一般的相互作用理论,如普通引力和Yang-Mills,我们可以利用自由场的结果来定义dS_4/Z_2中的适定扰动初值问题。

英文摘要:

We study gauge fields of arbitrary spin in de Sitter space. These include Yang-Mills fields and gravitons, as well as the higher-spin fields of Vasiliev theory. We focus on antipodally symmetric solutions to the field equations, i.e. ones that live on "elliptic" de Sitter space dS_4/Z_2. For free fields, we find spanning sets of such solutions, including boundary-to-bulk propagators. We find that free solutions on dS_4/Z_2 can only have one of the two types of boundary data at infinity, meaning that the boundary 2-point functions vanish. In Vasiliev theory, this property persists order by order in the interaction, i.e. the boundary n-point functions in dS_4/Z_2 all vanish. This implies that a higher-spin dS/CFT based on the Lorentzian dS_4/Z_2 action is empty. For more general interacting theories, such as ordinary gravity and Yang-Mills, we can use the free-field result to define a well-posed perturbative initial value problem in dS_4/Z_2.

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