Instantons and the Hartle-Hawking-Maldacena Proposal for dS/CFT

TL;DR

This paper tests the Maldacena proposal for the quantum state in de Sitter space by comparing scalar instanton actions in de Sitter and Euclidean Anti-de Sitter spaces, revealing a deep geometric correspondence.

Contribution

It introduces novel instanton solutions in de Sitter space with mixed boundary conditions and establishes a geometric relationship between instantons in de Sitter and Euclidean AdS spaces.

Findings

Instanton actions in de Sitter and EAdS spaces agree under analytic continuation.

Instantons on S^4 compute the volume of EAdS_4, and vice versa.

The results have implications for higher-spin holography.

Abstract

We test the Maldacena proposal for the Hartle-Hawking late time quantum state in an asymptotically de Sitter universe. In particular, we calculate the on-shell action for scalar instantons on the southern hemisphere of the four-sphere and compare the result with the renormalized on-shell action for scalar instantons in EAdS$_4$. The two results agree provided the corresponding instanton moduli as well as the curvature radii are analytically continued. The instanton solutions in de Sitter are novel and satisfy mixed boundary conditions. We also point out that instantons on $S^4$ calculate the regularized volume of EAdS$_4$, while instantons on EAdS$_4$ calculate the volume of $S^4$, where the boundary condition of the instanton in one space is identified with the radius of curvature of the other. We briefly discuss the implications of the above geometric property of instantons for higher-spin holography.