Infra-red effects of Non-linear sigma model in de Sitter space

TL;DR

This paper investigates infra-red effects in non-linear sigma models in de Sitter space, showing cancellation of leading infra-red logarithms in certain models and growth of effects in others, indicating potential symmetry breaking mechanisms.

Contribution

It demonstrates the cancellation of leading infra-red logarithms in generic non-linear sigma models and explores conditions under which infra-red effects grow, affecting de Sitter symmetry.

Findings

Leading infra-red logarithms cancel to all orders in generic models.

In N sphere target space, de Sitter symmetry is preserved at large N.

Infra-red logarithms appear at three loops for less symmetric target spaces, but can be canceled by counter terms.

Abstract

We extend our investigation on a possible de Sitter symmetry breaking mechanism in non-linear sigma models. The scale invariance of the quantum fluctuations could make the cosmological constant time dependent signaling the de Sitter symmetry breaking. To understand such a symmetry breaking mechanism, we investigate the energy-momentum tensor. We show that the leading infra-red logarithms cancel to all orders in perturbation theory in a generic non-linear sigma model. When the target space is an N sphere, the de Sitter symmetry is preserved in the large N limit. For a less symmetric target space, the infra-red logarithms appear at the three loop level. However there is a counter term to precisely cancel it. The leading infra-red logarithms do not cancel for higher derivative interactions. We investigate such a model in which the infra-red logarithms first appear at the three loop level. A nonperturbative investigation in the large N limit shows that they eventually grow as large as the one loop effect.