Linearized transverse diffeomorphism invariant spin-2 theories via gauge invariants

TL;DR

This paper develops a new class of stable, gauge-invariant spin-2 theories with a specific particle spectrum, using a Lagrangian approach and Bardeen variables, and proposes a nonlinear completion.

Contribution

It introduces a novel class of linearized transverse diffeomorphism invariant spin-2 models with a unique spectrum and a proposed nonlinear extension.

Findings

Identified a spectrum with one massless spin-2 and two massless scalars.

Developed a gauge-invariant, Lagrangian method using Bardeen variables for spectrum analysis.

Proposed a nonlinear completion with a dynamical metric field.

Abstract

We analyze the particle spectrum of a second-order (in derivatives) theory based on a rank-2 tensor field with both symmetric and antisymmetric components. By demanding the existence of a propagating massless spin-2 particle and invariance under linearized transverse diffeomorphisms, we derive a new class of stable models with two massless scalars and a single massless spin-2 particle. A natural non linear completion is proposed in terms of a dynamical metric field. The identification of the spectrum is carried out using a fully Lagrangian, gauge-invariant approach which makes use of Bardeen variables in a constructive manner. The approach significantly reduces the number of steps in the spectrum determination in some cases.