De Sitter Gravity and Liouville Theory

TL;DR

The paper establishes a concrete dS3 gravity Liouville duality by matching Kerr-de Sitter bulk solutions to Liouville vertex operators, with the central charge $c = 3l/(2G)$ and a dictionary that maps bulk masses to Liouville dimensions. Classical Liouville dimensions reproduce bulk masses while quantum dimensions align with Brown-York masses, and the Seiberg bound translates to an upper bound on bulk masses; horizons correspond to microscopic Liouville states and non horizon solutions to macroscopic states. The dual CFT is not thermal, and de Sitter entropy is interpreted as Liouville momentum rather than a statistical count. Overall, the work provides a concrete test of the dS3/CFT2 correspondence and clarifies the entropy interpretation within the Liouville framework.

Abstract

We show that the spectrum of conical defects in three-dimensional de Sitter space is in one-to-one correspondence with the spectrum of vertex operators in Liouville conformal field theory. The classical conformal dimensions of vertex operators are equal to the masses of the classical point particles in dS_3 that cause the conical defect. The quantum dimensions instead are shown to coincide with the mass of the Kerr-dS_3 solution computed with the Brown-York stress tensor. Therefore classical de Sitter gravity encodes the quantum properties of Liouville theory. The equality of the gravitational and the Liouville stress tensor provides a further check of this correspondence. The Seiberg bound for vertex operators translates on the bulk side into an upper mass bound for classical point particles. Bulk solutions with cosmological event horizons correspond to microscopic Liouville states, whereas those without horizons correspond to macroscopic (normalizable) states. We also comment on recent criticism by Dyson, Lindesay and Susskind, and point out that the contradictions found by these authors may be resolved if the dual CFT is not able to capture the thermal nature of de Sitter space. Indeed we find that on the CFT side, de Sitter entropy is merely Liouville momentum, and thus has no statistical interpretation in this approach.