Holography in de Sitter Space via Chern-Simons Gauge Theory

TL;DR

This work proposes a concrete dS/CFT framework in three dimensions by relating Euclidean gravity on S^3 to a pair of SU(2) Chern-Simons theories and identifying a novel holographic limit k -> -2 in the SU(2) WZW model that yields the correct semiclassical gravity results. It establishes a dictionary between CS partition functions (via modular S-matrix elements) and gravitational observables such as energies, entropies, and entanglement measures, and extends the construction to higher spin gravity through SU(N) Chern-Simons theories and coset dualities. The results provide a coherent holographic picture for dS_3, show exact matches for black hole and entanglement entropy, and point toward a broader higher-spin dS/CFT correspondence governed by W_N and W_infty symmetries. Future work includes computing correlation functions, quantum corrections, and a Lorentzian continuation to connect with the Lorentzian dS spacetime.

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.

Figures (1)

• Figure 1: The North [Left] and South [Right] hemisphere with two linked Wilson lines (red and green).