Radiatively stable ghost and tachyon freedom in Metric Affine Gravity

TL;DR

This paper identifies a stable, ghost- and tachyon-free sector in metric-affine gravity, stabilized by symmetries, and explores mass generation via a Stueckelberg extension, ensuring unitarity and causality without fine-tuning.

Contribution

It demonstrates the existence of a ghost- and tachyon-free sector in metric-affine gravity with symmetries that ensure stability without tuning, and introduces a mass mechanism through a Stueckelberg extension.

Findings

Existence of a ghost- and tachyon-free sector in metric-affine gravity.

Mass generation mechanism via Stueckelberg extension involving non-metricity.

Stable spectrum of operators in the extended model.

Abstract

We report the existence of a ghost- and tachyon-free sector in metric-affine theories of gravity, that is invariant under diffeomorphism and a particular abelian symmetry. In contrast with many studied cases in the literature, the constraints for unitarity and causality are granted by non-accidental symmetries and do not ask for further tuning, whose fate under renormalization would be unclear. Unsurprisingly, the minimal model is massless. We find that a mechanism to provide mass is accommodated by a simple Stueckelberg extension of metric-affine gravity involving the non-metricity tensor. A non-trivial result is that also such an extension describes a ghost- and tachyon-free dynamic stabilized by the same abelian symmetry. The resulting spectrum of the collective rank-3, rank-2, and rank-0 Lagrangian is investigated with the operators recently computed in the literature.