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Codimension two holography for wedges

Aug 6, 2020

28 pages

Published in:

Phys.Rev.D 102 (2020) 12, 126007

Published: Dec 3, 2020

e-Print:

2007.06800 [hep-th]

DOI:

10.1103/PhysRevD.102.126007

Report number:

YITP-20-91,
IPMU20-0079

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Abstract: (APS)

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 spacelike 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.

Note:

57 pages, 17 figures; v2: typos corrected, references added; v3: improved explanations, minor corrections; v4: comments added in section 2.1

String theory, quantum gravity, gauge/gravity duality
entropy: entanglement
anomaly: conformal
holography
AdS/CFT correspondence
correlation function
free energy
black hole: BTZ
membrane model
any-dimensional

References(71)

Figures(21)

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