Holography in de Sitter Space via Chern-Simons Gauge Theory

TL;DR

This paper proposes a holographic duality between three-dimensional de Sitter gravity and an SU(2) Chern-Simons gauge theory, establishing a connection with a WZW model and extending to higher spin theories.

Contribution

It introduces a novel holographic duality for de Sitter space using Chern-Simons gauge theories and extends the framework to higher spin gravity.

Findings

Chern-Simons theories reproduce Einstein gravity partition function on de Sitter space.

The dual CFT is an SU(2) WZW model at large central charge.

Evidence from coset CFT holography supports the duality.

Abstract

In this paper we propose a holographic duality for classical gravity on a three-dimensional de Sitter space. We first show that a pair of SU$(2)$ Chern-Simons gauge theories reproduces the classical partition function of Einstein gravity on a Euclidean de Sitter space, namely $\mathbb{S}^3$, when we take the limit where the level $k$ approaches $-2$. This implies that the CFT dual of gravity on a de Sitter space at the leading semi-classical order is given by an SU$(2)$ Wess-Zumino-Witten (WZW) model in the large central charge limit $k\to -2$. We give another evidence for this in the light of known holography for coset CFTs. We also present a higher spin gravity extension of our duality.