Unitarity of spin-2 theories with linearized Weyl symmetry in $D=2+1$

Abstract

Here we prove unitarity of the recently found fourth-order self-dual model of spin-2 by investigating the analytic structure of its propagator. The model describes massive particles of helicity +2 (or -2) in $D=2+1$ and corresponds to the quadratic truncation of a higher derivative topologically massive gravity about a flat background. It is an intriguing example of a theory where a term in the propagator of the form $1/[{\square }^2(\square -m^2)]$ does not lead to ghosts. The crucial role of the linearized Weyl symmetry in getting rid of the ghosts is pointed out. We use a peculiar pair of gauge conditions which fix the linearized reparametrizations and linearized Weyl symmetries separetely.

9 pages, no figures

References in corpus (6)

• Massive Gravity in Three Dimensions
• More on Massive 3D Gravity
• Ghost-free, finite, fourth order D=3 (alas) gravity
• On Unitarity of Massive Gravity in Three Dimensions
• A new spin-2 self-dual model in $D=2+1$
• Dual descriptions of spin two massive particles in $D=2+1$ via master actions

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