Codimension two holography for wedges

Ibrahim Akal; Yuya Kusuki; Tadashi Takayanagi; Zixia Wei

doi:10.1103/physrevd.102.126007

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arXiv · 2007.06800

Codimension two holography for wedges

Ibrahim Akal·Yuya Kusuki·Tadashi Takayanagi·Zixia Wei

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Abstract

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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Ibrahim Akal, Yuya Kusuki, Tadashi Takayanagi, Zixia Wei. 2020-07-14. Codimension two holography for wedges. https://doi.org/10.1103/physrevd.102.126007

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