Bound states of massive complex ghosts in superrenormalizable quantum gravity theories\

TL;DR

This paper explores the complex mass spectrum in superrenormalizable quantum gravity theories, showing that complex ghost states form bound states that could have significant cosmological implications.

Contribution

It demonstrates that superrenormalizable quantum gravity theories with complex spectra do not satisfy positivity and form bound states, revealing new aspects of ghost confinement.

Findings

Complex ghost states form bound states in toy models.

Theories with complex spectra violate positivity criteria.

Potential cosmological implications of ghost confinement.

Abstract

One of the remarkable differences between renormalizable quantum gravity with four-derivative action and its superrenormalizable polynomial generalizations is that the latter admit a more sophisticated particle mass spectrum. Already in the simplest superrenormalizable case, the theory has a six-derivative Lagrangian, admitting either a real or complex spectrum of masses. In the case of a real spectrum, there are the graviton, massive unphysical ghosts, and normal particles with masses exceeding the ones of the ghosts. It is also possible to have pairs of complex conjugate massive ghost-like particles. We show that in both cases, these theories do not admit a K\"all\'en-Lehmann representation and do not satisfy the positivity criterium of consistency in terms of the fields associated to those particles. In the main part of the work, using a relatively simple Euclidean scalar toy model, we show that the theory with complex spectrum forms bound states confining unphysical massive excitations into a normal composite particle. Finally, we discuss the cosmological implications of such a ghost confinement.