arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2006.02803hep-thgr-qcmath-phmath.MP
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拓扑AdS引力中的锥缺陷与全息

Conical defects and holography in topological AdS gravity

Jani Kastikainen

摘要:

我们研究余维,甚至圆锥形缺陷,包含沿缺陷的每个点周围的赤字立体角。我们表明,他们导致一个δ函数的贡献Lovelock标量,我们计算的贡献,通过两种方法。然后我们证明了这些余维偶亏在高维拓扑AdS引力(无挠的Lovelock-Chern-Simons引力)中表现为欧几里德膜解。该理论拥有一个全息外尔异常,是纯粹的A型和比例的洛夫洛克标量。利用缺陷贡献公式,证明了余维偶缺陷配分函数与余维偶膜壳作用之间的全息对偶.更具体地说,我们发现对数发散是匹配的,因为洛夫洛克-陈-西蒙斯作用量精确地定位在膜上。我们证明了对偶明确的边界上的一个球形缺陷作为一个余维甚至双曲膜扩展到散装。对于零膜张力,几何是欧几里德AdS空间的叶理,它提供了AdS-Rindler空间的单参数推广。

英文摘要:

We study codimension-even conical defects that contain a deficit solid angle around each point along the defect. We show that they lead to a delta function contribution to the Lovelock scalar and we compute the contribution by two methods. We then show that these codimension-even defects appear as Euclidean brane solutions in higher dimensional topological AdS gravity which is Lovelock-Chern-Simons gravity without torsion. The theory possesses a holographic Weyl anomaly that is purely of type-A and proportional to the Lovelock scalar. Using the formula for the defect contribution, we prove a holographic duality between codimension-even defect partition functions and codimension-even brane on-shell actions in Euclidean signature. More specifically, we find that the logarithmic divergences match, because the Lovelock-Chern-Simons action localizes on the brane exactly. We demonstrate the duality explicitly for a spherical defect on the boundary which extends as a codimension-even hyperbolic brane into the bulk. For vanishing brane tension, the geometry is a foliation of Euclidean AdS space that provides a one-parameter generalization of AdS-Rindler space.

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