Living with ghosts in Lorentz invariant theories

TL;DR

This paper explores the possibility that Lorentz invariant theories with ghost fields can have a long-lived vacuum state, analyzing decay rates and proposing nonlocal interactions to ensure consistency with observations.

Contribution

It demonstrates that ghost-containing theories can be stable over long times if interactions are nonlocal, especially in higher dimensions, and provides a concrete nonlocal interaction example.

Findings

Vacuum decay rate is finite and grows logarithmically in 2D.

Decay rate diverges in higher dimensions unless interactions are nonlocal.

A nonlocal gravitational interaction can satisfy observational constraints.

Abstract

We argue that theories with ghosts may have a long lived vacuum state even if all interactions are Lorentz preserving. In space-time dimension D = 2, we consider the tree level decay rate of the vacuum into ghosts and ordinary particles mediated by non-derivative interactions, showing that this is finite and logarithmically growing in time. For D > 2, the decay rate is divergent unless we assume that the interaction between ordinary matter and the ghost sector is soft in the UV, so that it can be described in terms of non-local form factors rather than point-like vertices. We provide an example of a nonlocal gravitational-strength interaction between the two sectors, which appears to satisfy all observational constraints.