dS${}_2$ Supergravity

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.

57 pages + appendices; v2: added references

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Cited by in corpus (7)

• The Virasoro Minimal String
• A microscopic realization of dS${}_3$
• de Sitter at all loops: the story of the Schwinger model
• New conformal-like symmetry of strictly massless fermions in four-dimensional de Sitter space
• The complex Liouville string: the gravitational path integral
• Unconventional conformal invariance of maximal depth partially massless fields on $d{S}_4$ and its relation to complex partially massless SUSY
• De Sitter Horizon Edge Partition Functions