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Cosmological quantum states of de Sitter-Schwarzschild are static patch partition functions

Published version
Peer-reviewed

Repository DOI


Change log

Authors

Blacker, MJ 
Hartnoll, SA 

Abstract

jats:titleAjats:scbstract</jats:sc> </jats:title>jats:pWe solve the Wheeler-DeWitt equation in the ‘cosmological interior’ (the past causal diamond of future infinity) of four dimensional dS-Schwarzschild spacetimes. Within minisuperspace there is a basis of solutions labelled by a constant jats:italicc</jats:italic>, conjugate to the mass of the black hole. We propose that these solutions are in correspondence with partition functions of a dual quantum mechanical theory where jats:italicc</jats:italic> plays the role of time. The quantum mechanical theory lives on worldtubes in the ‘static patch’ of dS-Schwarzschild, and the partition function is obtained by evolving the corresponding Wheeler-DeWitt wavefunction through the cosmological horizon, where a metric component jats:italicg</jats:italic>jats:subjats:italictt</jats:italic></jats:sub> changes sign. We establish that the dual theory admits a symmetry algebra given by a central extension of the Poincaré algebra jats:inline-formulajats:alternativesjats:tex-math$$ \mathfrak{e} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mie</mml:mi> </mml:math></jats:alternatives></jats:inline-formula>(1jats:italic,</jats:italic> 1) and that the entropy of the dS black hole is encoded as an averaging of the dual partition function over the background jats:italicg</jats:italic>jats:subjats:italictt</jats:italic></jats:sub>.</jats:p>

Description

Acknowledgements: It is a pleasure to acknowledge inspiring discussions with Dionysios Anninos, Diego Hofman, Albert Law and Ronak Soni. The work of S.A.H. is partially supported by Simons Investigator award #620869 and by STFC consolidated grant ST/T000694/1. M.J.B. was supported by a Gates Cambridge Scholarship (#OPP1144).

Keywords

4902 Mathematical Physics, 5107 Particle and High Energy Physics, 49 Mathematical Sciences, 51 Physical Sciences

Journal Title

Journal of High Energy Physics

Conference Name

Journal ISSN

1126-6708
1029-8479

Volume Title

2023

Publisher

Springer Science and Business Media LLC