CFT duals of three-dimensional de Sitter gravity

TL;DR

The paper proposes a concrete dS3/CFT2 holographic duality in which 3D gravity on de Sitter space is captured by a 2D CFT built from an SU(2) (and SU(N)) WZW model at critical level, complemented by a matter sector. In the classical limit the SU(N) current algebra dominates, yielding an imaginary central charge that matches the dS/CFT expectation, and the gravity partition functions on S3 are reproduced from CFT S-matrix data and conical defect geometries via a CS/WZW correspondence. The authors extend the construction to higher spin via SU(N) Chern-Simons gravity, relate the dual description to Liouville/Toda CFTs in the Lorentzian regime, and connect the framework to Gaberdiel-Gopakumar duality through analytic continuation, with tests through partition functions, two-point functions, and holographic entanglement entropy. They also discuss the spectrum of bulk objects, possible quantum corrections, and the significance for understanding quantum gravity in de Sitter space. The work provides a detailed, testable microscopic realization of dS3/CFT2 and lays groundwork for future exploration of holography in cosmological spacetimes.

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.

Figures (6)

• Figure 1: A sketch of the dS/CFT correspondence. $\phi$ denotes all bulk fields and $\phi^{(0)}$ does their values at the asymptotic boundary (i.e. future infinity).
• Figure 2: A sketch of the path integral in the right-hand side of \ref{['square']}. The red and blue regions represent the Euclidean $(\mathbb{B}^3)$ and Lorentzian $(\text{dS}_3)$ part of Hartle-Hawking wave functional $\Psi_{\text{dS}}$, respectively. The Lorentzian parts of $\Psi_{\text{dS}}$ and its dual $\Psi_{\text{dS}}^*$ cancel out, leaving only the Euclidean part $Z_{\text{G}}\left[\mathbb{S}^3\right]$.
• Figure 3: Sketches of the computations of partition functions in Chern-Simons theory on $\mathbb{S}^3$.
• Figure 4: The North (left) and South (right) hemisphere with two linked Wilson lines (orange and blue).
• Figure 5: The profile of a geodesic which connects two points on the future boundary in the Lorentzian dS$_3$ with an initial Euclidean hemisphere, following from the standard Hartle-Hawking prescription.