On higher spin analogues of linearized Topologically Massive Gravity and linearized "New Massive Gravity"

Abstract

We suggest a new spin-4 self-dual model (parity singlet) and a new spin-4 parity doublet in $D=2+1$. They are of higher order in derivatives and are described by a totally symmetric rank-4 tensor without extra auxiliary fields. Despite the higher derivatives they are ghost free. We find gauge invariant field combinations which allow us to show that the canonical structure of the spin-4 (spin-3) models follows the same pattern of its spin-2 (spin-1) counterpart after field redefinitions. For $s=1,2,3,4$, the spin-$s$ self-dual models of order $2s-1$ and the doublet models of order $2s$ can be written in terms of three gauge invariants. The cases $s=3$ and $s=4$ suggest a restricted conformal higher spin symmetry as a principle for defining linearized topologically massive gravity and linearized "New Massive Gravity" for arbitrary integer spins. A key role in our approach is played by the fact that the Cotton tensor in $D=2+1$ has only two independent components for any integer spin.

arXiv comment28 pages, no figures, references added, few sentences slightly changed, to appear in Phys. Rev. D

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Cited by in corpus (5)

• Higher-spin gauge theories in three spacetime dimensions
• Quasi-topological mass generation for 3D linearized gravity
• Massive Higher-Spin Fields in the Fractional Quantum Hall Effect
• Linearized transverse diffeomorphism invariant spin-2 theories via gauge invariants
• Reaching out a "geometrical" description for spin-4 self-dual models in $D=2+1$