Holography in de Sitter Space via Chern-Simons Gauge Theory

In this Letter, 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 conformal field theory (CFT) dual of gravity on a de Sitter space at the leading semiclassical order is given by an SU(2) Wess-Zumino-Witten 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.

Figure 1

The north (left) and south (right) hemisphere with two linked Wilson lines (red and green).