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

TL;DR

This paper explores different formulations of spin two massive particles in 2+1 dimensions, establishing dualities and quantum equivalences among models with various derivative orders and topological terms.

Contribution

It introduces a master action linking first, second, and third order self-dual models and proves quantum equivalence of certain self-dual models with a generalized model including Einstein-Hilbert, Chern-Simons, and Fierz-Pauli terms.

Findings

Decoupling of redundant degrees of freedom in covariant descriptions.

Explicit dual maps between different order models.

Quantum equivalence of self-dual models with a generalized model.

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.