Unitarity of Weyl-Invariant New Massive Gravity and Generation of Graviton Mass via Symmetry Breaking

TL;DR

This paper analyzes the unitarity and particle spectrum of a Weyl-invariant massive gravity theory in 2+1 dimensions, showing it describes unitary massive and massless particles under certain conditions and discusses mass generation via symmetry breaking.

Contribution

It provides a detailed perturbative unitarity analysis of Weyl-invariant new massive gravity, revealing conditions for unitarity and mechanisms for graviton mass generation.

Findings

The theory describes unitary massive spin-2, spin-1, and spin-0 particles in AdS and flat backgrounds.

Unitarity fails in de Sitter space.

Masses are generated through spontaneous or radiative symmetry breaking.

Abstract

We give a detailed analysis of the particle spectrum and the perturbative unitarity of the recently introduced Weyl-invariant version of the new massive gravity in 2+1 dimensions. By computing the action up to second order in the fluctuations of the metric, the gauge and the scalar fields around the anti-de Sitter (AdS) and flat vacua, we find that the theory describes unitary (tachyon and ghost-free) massive spin-2, massive (or massless) spin-1 and massless spin-0 excitations for certain ranges of the dimensionless parameters. The theory is not unitary in de Sitter space. Scale invariance is either broken spontaneously (in AdS background) or radiatively (in flat background) and hence the masses of the particles are generated either spontaneously or at the second loop order.