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

Abstract

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.

title and abstract slightly modified, 3 references added, comments on interactions included

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• Generalized soldering of $\pm 2$ helicity states in $D=2+1$
• Unitarity of spin-2 theories with linearized Weyl symmetry in $D=2+1$
• Dual descriptions of massive spin-3 particles in $D=2+1$ via Noether gauge embedment
• Duality of parity doublets of helicity $\pm 2$ in $D=2+1$
• Higher order self-dual models for spin-3 particles in $D=2+1$
• Dual equivalence between self-dual and topologically massive $B\wedge F$ models coupled to matter in $3+1$ dimensions
• Master actions for linearized massive gravity models in 3-D
• 3D black holes on a 2-brane in 4D Minkowski space
• Master actions for massive spin-3 particles in D=2+1
• Weyl and transverse diffeomorphism invariant spin-2 models in D=2+1
• Self-dual formulations of d=3 gravity theories in the path-integral framework
• Dual composition of odd-dimensional models
• Reaching out a "geometrical" description for spin-4 self-dual models in $D=2+1$