On Lorentz-invariant bi-spin-2 theories

TL;DR

This paper explores Lorentz-invariant quadratic actions involving two symmetric tensor fields, classifies theories with seven degrees of freedom, and discovers two novel theories with unique mass interactions enabled by transverse diffeomorphism invariance.

Contribution

It introduces two new bi-spin-2 theories that are not derivable from linearized Hassan-Rosen bigravity, expanding the landscape of Lorentz-invariant tensor field theories.

Findings

Identified two new theories with seven degrees of freedom.

Demonstrated these theories cannot be obtained from linearized Hassan-Rosen bigravity.

Showed that transverse diffeomorphism invariance allows new mass interactions.

Abstract

We investigate a Lorentz invariant action which is quadratic in two rank-2 symmetric tensor fields in Minkowski spacetime. We apply a scalar-vector-tensor decomposition to two tensor fields by virtue of 3-dimensional rotation-invariance of Minkowski spacetime and classify theories with seven degrees of freedom based on the Hamiltonian analysis. We find two new theories, which cannot be mapped from the linearized Hassan-Rosen bigravity. In these theories, the new mass interactions can be allowed thanks to the transverse diffeomorphism invariance of action.