Hubeny, V. E. and Rangamani, M. and Takayanagi, T. (2007) 'A covariant holographic entanglement entropy proposal.', Journal of high energy physics., 2007 (07). 062.
With an aim towards understanding the time-dependence of entanglement entropy in generic quantum field theories, we propose a covariant generalization of the holographic entanglement entropy proposal of hep-th/0603001. Apart from providing several examples of possible covariant generalizations, we study a particular construction based on light-sheets, motivated in similar spirit to the covariant entropy bound underlying the holographic principle. In particular, we argue that the entanglement entropy associated with a specified region on the boundary in the context of the AdS/CFT correspondence is given by the area of a co-dimension two bulk surface with vanishing expansions of null geodesics. We demonstrate our construction with several examples to illustrate its reduction to the holographic entanglement entropy proposal in static spacetimes. We further show how this proposal may be used to understand the time evolution of entanglement entropy in a time varying QFT state dual to a collapsing black hole background. Finally, we use our proposal to argue that the Euclidean wormhole geometries with multiple boundaries should be regarded as states in a non-interacting but entangled set of QFTs, one associated to each boundary.
|Keywords:||AdS-CFT Correspondence, Gauge-gravity correspondence.|
|Full text:||PDF (arXiv version) - Other (792Kb)|
|Publisher Web site:||http://dx.doi.org/10.1088/1126-6708/2007/07/062|
|Publisher statement:||© SISSA 2007. Published by IOP Publishing for SISSA. This is an author-created, un-copyedited version of an article accepted for publication in Journal of high energy physics. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at 10.1088/1126-6708/2007/07/062.|
|Record Created:||23 Jul 2007|
|Last Modified:||17 Jun 2015 12:26|
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