Breaking of de Sitter Symmetry

TL;DR

This paper demonstrates that interactions in a scalar field theory on de Sitter space lead to explicit breaking of de Sitter symmetry, with anomalies arising at one loop in higher dimensions.

Contribution

It provides a detailed analysis of how interacting scalar fields break de Sitter symmetry, including explicit solutions in (1+1) dimensions and anomaly calculations in higher dimensions.

Findings

Massless boson with sine-Gordon potential maps to free massive fermion, breaking symmetry.

One-loop anomalies prevent conservation of de Sitter currents in higher dimensions.

Explicit symmetry breaking occurs due to interactions in de Sitter space.

Abstract

We show that an interacting spin-0 field on a de Sitter space background will break the underlying de Sitter symmetry. This is done first for a (1+1) de Sitter space where a boson-fermion correspondence permits us to solve certain interacting theories by transforming them into free ones of opposite statistics. A massless boson interacting by a sine-Gordon potential is shown to be equivalent to a free massive fermion with the mass depending on the de Sitter time thus breaking the symmetry explicitly. We then show that for larger dimensions and any boson potential, to one loop, an anomaly develops and the currents generating the de Sitter transformations are not conserved.