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arXiv 2007.06800hep-thcond-mat.stat-mechgr-qc
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楔的余维二全息术

Codimension two holography for wedges

Ibrahim Akal, Yuya Kusuki, Tadashi Takayanagi, Zixia Wei

摘要:

我们提出了一个在$d+1$维楔形时空上的引力理论和一个位于楔形角上的$d-1$维CFT之间的余维2全息。作为AdS/CFT的推广,我们解释了如何从引力计算对偶CFT的自由能、纠缠熵和关联函数。在这种楔形全息术中,全息纠缠熵是用双重极小化方法计算的。特别地,对于四维引力场($d=3$),我们得到了二维的CFT和全息的纠缠熵,很好地再现了全息共形反常所期望的结果.我们还讨论了一个低维的例子($d=2$),并发现一个普遍的量自然产生的重力,这是类似的边界熵。此外,我们还考虑了洛伦兹AdS中楔形区域上的引力,它与具有类空边界的CFT是对偶的。我们制定了这种新的全息和计算全息纠缠熵通过一个威克旋转的AdS/BCFT结构。通过共形映射,这个楔形时空被映射到一个几何形状中,在这个几何形状中,一个虚无的气泡在时间演化中膨胀。我们通过CFT计算再现了这种引力对偶的全息纠缠熵。

英文摘要:

We propose a codimension two holography between a gravitational theory on a $d+1$ dimensional wedge spacetime and a $d-1$ dimensional CFT which lives on the corner of the wedge. Formulating this as a generalization of AdS/CFT, we explain how to compute the free energy, entanglement entropy and correlation functions of the dual CFTs from gravity. In this wedge holography, the holographic entanglement entropy is computed by a double minimization procedure. Especially, for a four dimensional gravity ($d=3$), we obtain a two dimensional CFT and the holographic entanglement entropy perfectly reproduces the known result expected from the holographic conformal anomaly. We also discuss a lower dimensional example ($d=2$) and find that a universal quantity naturally arises from gravity, which is analogous to the boundary entropy. Moreover, we consider a gravity on a wedge region in Lorentzian AdS, which is expected to be dual to a CFT with a space-like boundary. We formulate this new holography and compute the holographic entanglement entropy via a Wick rotation of the AdS/BCFT construction. Via a conformal map, this wedge spacetime is mapped into a geometry where a bubble-of-nothing expands under time evolution. We reproduce the holographic entanglement entropy for this gravity dual via CFT calculations.

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