dS/CFT Correspondence from a Holographic Description of Massless Scalar Fields in Minkowski Space-Time

TL;DR

This paper establishes a holographic duality between massless scalar fields in Minkowski space and conformally coupled scalars on (A)dS space, providing a Minkowski space realization of the dS/CFT correspondence.

Contribution

It derives the holographic dual of massless scalars in Minkowski space and connects it to the (A)dS/CFT correspondence through a one-to-one map.

Findings

Holographic dual action on boundary t=0 matches (A)dS/CFT results

Establishes a one-to-one map between Minkowski and (A)dS scalar fields

Provides a Minkowski space perspective on dS/CFT correspondence

Abstract

We solve Klein-Gordon equation for massless scalars on d+1 dimensional Minkowski (Euclidean) space in terms of the Cauchy data on the hypersurface t=0. By inserting the solution into the action of massless scalars in Minkowski (Euclidean) space we obtain the action of dual theory on the boundary t=0 which is exactly the holographic dual of conformally coupled scalars on d+1 dimensional (Euclidean anti) de Sitter space obtained in (A)dS/CFT correspondence. The observed equivalence of dual theories is explained using the one-to-one map between conformally coupled scalar fields on Minkowski (Euclidean) space and (Euclidean anti) de Sitter space which is an isomorphism between the hypersurface t=0 of Minkowski (Euclidean) space and the boundary of (A)dS space.