S. Deser, S. Ertl, D. Grumiller
Schouten gravity, a (pure) quadratic curvature three-dimensional model, provides a unique example of symmetry breaking through the clash between its two local, conformal and coordinate, invariances. Their co-existence at linearized level underlies this fourth derivative metric system's "miraculous" transmutation into single ghost-free vector excitation, or equivalently to a propagating torsion with non-propagating metric. Nonlinearly, however, conformal- is necessarily sacrificed to coordinate-invariance. After a concise derivation of this fourth order action's initial photon transmutation, we exhibit the nonlinear obstructions and their effects, in particular, introduction of propagator-less variables.
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http://arxiv.org/abs/1208.0339
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