Virasoro generators and the dS_3/CFT_2 correspondence

TL;DR

This paper explores the quantization of scalar fields in three-dimensional de Sitter space, extending symmetry algebras to Virasoro and elucidating the dS/CFT correspondence through explicit charge actions.

Contribution

It introduces a method to extend the isometry algebra to a full Virasoro algebra in dS space and clarifies the dS/CFT correspondence with explicit charge representations.

Findings

Virasoro algebra with expected central charge derived

Explicit expressions for Noether currents obtained

Action of Virasoro charges on boundary CFT states elucidated

Abstract

We discuss the quantization of a scalar field in three-dimensional asymptotic de Sitter space. We obtain explicit expressions for the Noether currents generating the isometry group in terms of the modes of the scalar field and the Liouville gravitational field. We extend the SL(2,C) algebra of the Noether charges to a full Virasoro algebra by introducing non-local conserved charges. The Virasoro algebra has the expected central charge in the weak coupling limit (large central charge c=3l/2G, where l is the dS radius and G is Newton's constant). We derive the action of the Virasoro charges on states in the boundary CFT thus elucidating the dS/CFT correspondence.