Abstract
We construct two-dimensional supergravity theories endowed with a positive cosmological constant, that admit de Sitter vacua. We consider the cases of \( \mathcal{N} \) = 1 as well as \( \mathcal{N} \) = 2 supersymmetry, and couple the supergravity to a superconformal field theory with the same amount of supersymmetry. Upon fixing a supersymmetric extension of the Weyl gauge, the theories are captured, at the quantum level, by supersymmetric extensions of timelike Liouville theory with \( \mathcal{N} \) = 1 and \( \mathcal{N} \) = 2 supersymmetry respectively. The theories exhibit good ultraviolet properties and are amenable to a variety of techniques such as systematic loop expansions and, in the \( \mathcal{N} \) = 2 case, supersymmetric localization. Our constructions offer a novel path toward a precise treatment of the Euclidean gravitational path integral for de Sitter, and in turn, the Gibbons-Hawking entropy of the de Sitter horizon. We argue that the supersymmetric localization method applied to the \( \mathcal{N} \) = 2 theory must receive contributions from boundary terms in configuration space. We also discuss how these theories overcome several obstructions that appear upon combining de Sitter space with supersymmetry.
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Acknowledgments
We are grateful to Tarek Anous, Francesco Benini, Davide Cassani, Lorenz Eberhardt, Jackson Fliss, Sameer Murthy, Luigi Tizzano, David Tong, and Stathis Vitouladitis for helpful discussions. BM is supported in part by the Simons Foundation Grant No. 385602 and the Natural Sciences and Engineering Research Council of Canada (NSERC), funding reference number SAPIN/00047-2020. The work of PBG has been supported by the ERC Consolidator Grant N. 681908, “Quantum black holes: a macroscopic window into the microstructure of gravity”, by the STFC grant ST/P000258/1, and by the Royal Society Grant RSWF/R3/183010. D.A. is funded by the Royal Society under the grant The Atoms of a deSitter Universe. PBG gratefully acknowledges support from the Simons Center for Geometry and Physics, Stony Brook University at which some of the research for this paper was performed.
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Anninos, D., Genolini, P.B. & Mühlmann, B. dS2 supergravity. J. High Energ. Phys. 2023, 145 (2023). https://doi.org/10.1007/JHEP11(2023)145
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DOI: https://doi.org/10.1007/JHEP11(2023)145