Topological surprises in de Sitter QFT in two-dimensions

TL;DR

This paper reveals how topological differences in two-dimensional de Sitter spacetime lead to fundamentally different quantum field theories, lacking typical features like the Bunch-Davies vacuum and Hawking-Gibbons thermal states.

Contribution

It demonstrates the impact of global topology on quantum field theory constructions in de Sitter space, highlighting effects not seen in simply connected models.

Findings

Local commutators are identical in both models.

Global topology alters the existence of the Bunch-Davies vacuum.

No Hawking-Gibbons thermal state in the topologically nontrivial case.

Abstract

Motivated by the study of soluble models of quantum field theory, we illustrate a new type of topological effect by comparing the constructions of canonical Klein-Gordon quantum fields on the two-dimensional de Sitter spacetime as opposed to its double covering. We show that the while commutators of the two fields coincide locally, the global topological differences make the theories drastically different. Many of the well-known features of de Sitter quantum field theory disappear. In particular there is nothing like a Bunch-Davies vacuum. Correspondingly, even though the local horizon structure is the same for the two universes there is no Hawking - Gibbons thermal state. Finally, there is no complementary series of fields.