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

Abstract

Here we prove unitarity of the recently found fourth-order (in derivatives) 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 dimensions 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 separately.