Massive spin 3 and Metric-Affine Gravity

TL;DR

This paper explores a symmetric metric-affine gravity theory with a non-metric connection, demonstrating that it can support healthy propagation of a spin-three field at the linearized level, which is a novel feature.

Contribution

It shows that symmetric metric-affine gravity can include a propagating spin-three degree of freedom with proper parameter choices, a new insight into higher-spin gravity models.

Findings

The spin-three field can propagate healthily at the linearized level.

Parameter tuning allows for stable spin-three and spin-zero modes.

The theory extends the landscape of consistent higher-spin gravitational models.

Abstract

Symmetric Metric-Affine Gravity is a theory of gravity with an independent non-metric connection, and zero torsion. It can be thought of as ordinary metric gravity coupled to a rank-three tensor Q, symmetric in one pair of indices. This field carries a spin-three degree of freedom. We find that, in contrast to the totally symmetric case, it is possible to arrange the parameters in the Lagrangian, so that, at the linearized level, the spin-three state, either alone or in combination with a spin-0 state, has a healthy propagation.