CFT duals of three-dimensional de Sitter gravity

TL;DR

This paper proposes a dS/CFT duality linking 2D CFTs, specifically SU(N) WZW models at critical levels, to 3D de Sitter gravity, supported by partition function matches and analysis of correlators and entanglement entropy.

Contribution

It introduces a new class of dS/CFT dualities involving SU(N) WZW models at critical levels and higher-spin gravity, with concrete evidence from partition functions and correlation functions.

Findings

Classical gravity partition functions match CFT calculations.

Two-point functions and entanglement entropy are analyzed within the duality.

Duality relations in higher-spin holography support the proposed correspondence.

Abstract

We present a class of dS/CFT correspondence between two-dimensional CFTs and three-dimensional de Sitter spaces. We argue that such a CFT includes an SU$(2)$ WZW model in the critical level limit $k\to -2$, which corresponds to the classical gravity limit. We can generalize this dS/CFT by considering the SU$(N)$ WZW model in the critical level limit $k\to -N$, dual to the higher-spin gravity on a three-dimensional de Sitter space. We confirm that under this proposed duality the classical partition function in the gravity side can be reproduced from CFT calculations. We also point out a duality relation known in higher-spin holography provides further evidence. Moreover, we analyze two-point functions and entanglement entropy in our dS/CFT correspondence. Possible spectrum and quantum corrections in the gravity theory are discussed.