Dual descriptions of spin-two massive particles in D=2+1 via master actions
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In the first part of this work we show the decoupling (up to contact terms) of redundant degrees of freedom which appear in the covariant description of spin-two massive particles in D=2+1. We make use of a master action which interpolates, without solving any constraints, between a first-, second-, and third-order (in derivatives) self-dual model. An explicit dual map between those models is derived. In our approach the absence of ghosts in the third-order self-dual model, which corresponds to a quadratic truncation of topologically massive gravity, is due to the triviality (no particle content) of the Einstein-Hilbert action in D=2+1. In the second part of the work, also in D=2+1, we prove the quantum equivalence of the gauge invariant sector of a couple of self-dual models of opposite helicities (+2 and -2) and masses m(+) and m(-) to a generalized self-dual model which contains a quadratic Einstein-Hilbert action, a Chern-Simons term of first order, and a Fierz-Pauli mass term. The use of a first-order Chern-Simons term instead of a third-order one avoids conflicts with the sign of the Einstein-Hilbert action.