Holography in de Sitter Space via Chern-Simons Gauge Theory

Abstract

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 S³, 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→−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.