dS/CFT Correspondence in Two Dimensions

TL;DR

This paper explores the quantization of a scalar particle in two-dimensional de Sitter space and constructs a conformal quantum mechanical model on its boundary, aligning boundary correlators with bulk Green functions.

Contribution

It introduces an explicit conformal quantum mechanical model for 2D de Sitter space and demonstrates the matching of boundary correlators with bulk Green functions.

Findings

Explicit generators of the conformal group are constructed.

Eigenvalues of the Hamiltonian are calculated.

Two-point correlators match bulk Green functions.

Abstract

We discuss the quantization of a scalar particle moving in two-dimensional de Sitter space. We construct the conformal quantum mechanical model on the asymptotic boundary of de Sitter space in the infinite past. We obtain explicit expressions for the generators of the conformal group and calculate the eigenvalues of the Hamiltonian. We also show that two-point correlators are in agreement with the Green function one obtains from the wave equation in the bulk de Sitter space.