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Timelike entanglement entropy in dS3/CFT2

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Jiang, X 
Wang, P 
Wu, H 
Yang, H 


jats:titleAjats:scbstract</jats:sc> </jats:title>jats:pIn the context of dSjats:sub3</jats:sub>/CFTjats:sub2</jats:sub>, we propose a timelike entanglement entropy defined by the renormalization group flow. This timelike entanglement entropy is calculated in CFT by using the Callan-Symanzik equation. We find an exact match between this entanglement entropy and the length of a timelike geodesic connecting two different spacelike surfaces in dSjats:sub3</jats:sub>. The counterpart of this entanglement entropy in AdSjats:sub3</jats:sub> is a spacelike one, also induced by RG flow and extends all the way into the bulk of AdSjats:sub3</jats:sub>. As a result, in both AdSjats:sub3</jats:sub>/CFTjats:sub2</jats:sub> and dSjats:sub3</jats:sub>/CFTjats:sub2</jats:sub>, there exist exactly three entanglement entropies, providing precisely sufficient information to reconstruct the three-dimensional bulk geometry.</jats:p>


Acknowledgements: This work is supported in part by NSFC (Grant No. 12275183, 12275184,12105191 and 11875196). HW is partly supported by discussions arising from the DAMTP workshop “Quantum de Sitter Universe”, funded by the Gravity Theory Trust and the Centre for Theoretical Cosmology. HW is also supported by the International Visiting Program for Excellent Young Scholars of Sichuan University.


AdS-CFT Correspondence, Holography and Hydrodynamics, de Sitter space

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Journal of High Energy Physics

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Springer Science and Business Media LLC