Conformal Vacuum of dS$_4\times \mathbb R$ with Oppositely Oriented Boundaries

TL;DR

This paper constructs a novel dS$_4 imes \\mathbb R$ spacetime with oppositely oriented boundaries, revealing a new vacuum state that is conformally related to a non-orientable AdS$_3$ spacetime, but is perturbatively unstable.

Contribution

It introduces a new asymptotically dS$_4$ quotient spacetime with opposite boundary orientations and analyzes its vacuum state and holographic dual, revealing instability issues.

Findings

The spacetime has a lightlike singularity separating antipodal regions.

The vacuum state is conformal to an AdS$_3$ spacetime with an S$^2$ bundle.

The vacuum exhibits perturbative instability due to a vanishing Hagedorn temperature.

Abstract

We derive a dS$_4 \times \mathbb R$ quotient spacetime that is asymptotically dS$_4$, where the quotient makes its past boundary oppositely oriented relative to its future boundary. This introduces a lightlike singularity that severs the antipodes of the spacetime and simplifies its global vacuum to a trivial product on antipodal static patches. We show that this state is conformal to the vacuum of an infinite orientable cover of a non-orientable AdS$_3$ spacetime with an S$^2$ bundle. The vacuum's separability extends to its holographic dual, which is a product of Cardy states. We find that this candidate dS$_4$ vacuum state is perturbatively unstable within quantum gravity due to a vanishing Hagedorn temperature.