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Dual descriptions of spin-two massive particles in D = 2 + 1 via master actions

2009; American Physical Society; Volume: 79; Issue: 4 Linguagem: Inglês

10.1103/physrevd.79.045025

1550-7998

D. Dalmazi, E. L. Mendonça,

Noncommutative and Quantum Gravity Theories

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 $\ensuremath{-}2$) and masses ${m}_{+}$ and ${m}_{\ensuremath{-}}$ 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.