Holography in de Sitter Space via Chern-Simons Gauge Theory

Understand

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.