Journal
CLASSICAL AND QUANTUM GRAVITY
Volume 32, Issue 6, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/0264-9381/32/6/065011
Keywords
AdS/CFT; entanglement entropy; conformal field theory; black holes
Categories
Funding
- National Science Foundation [PHY11-25915]
- FQXi grant [FRP3-1338]
- University of California
- STFC [ST/L00044X/1] Funding Source: UKRI
- Science and Technology Facilities Council [ST/L00044X/1] Funding Source: researchfish
- Direct For Mathematical & Physical Scien
- Division Of Physics [1205500] Funding Source: National Science Foundation
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We study and construct spacetimes, dubbed planar AdS-dS-wormholes, satisfying the null energy condition and having two asymptotically AdS boundaries connected through a (non-traversable) inflating wormhole. As for other wormholes, it is natural to expect dual descriptions in terms of two disconnected conformal field theories (CFTs) in appropriate entangled states. But for our cases, certain expected bulk entangling surfaces used by the Hubeny-Rangamani-Takayanagi (HRT) prescription to compute CFT entropy do not exist. In particular, no real codimension-2 extremal surface can run from one end of the wormhole to the other. According to HRT, the mutual information between any two finite-sized subregions (one in each CFT) must then vanish at leading order in large N-though the leading-order mutual information per unit area between the two CFTs taken as wholes may be nonzero. Some planar AdS-dS-wormholes also fail to have plane-symmetric surfaces that would compute the total entropy of either CFT. We suggest this to remain true of less-symmetric surfaces so that the HRT entropy is ill-defined and some modified prescription is required. It may be possible to simply extend HRT or the closely-related maximin construction by a limiting procedure, though complex extremal surfaces could also play an important role.
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