dS$_2$ Supergravity

TL;DR

This paper constructs two-dimensional supergravity theories with positive cosmological constant that admit de Sitter vacua, coupling them to superconformal field theories, and explores their quantum properties and implications for de Sitter entropy.

Contribution

It introduces novel 2D supergravity models with de Sitter vacua coupled to superconformal theories, analyzed via supersymmetric extensions of Liouville theory and localization techniques.

Findings

Theories have good ultraviolet properties.

Supersymmetric localization involves boundary contributions.

Provides a new approach to Euclidean de Sitter quantum gravity.

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.