Topologically massive higher spin gauge theories

DOI10.1007/JHEP10(2018)160zbMATH Open1402.83108arXiv1806.06643OpenAlexW3106124367MaRDI QIDQ1627384

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Publication date: 22 November 2018

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Abstract: We elaborate on conformal higher-spin gauge theory in three-dimensional (3D) curved space. For any integer $n>2$ we introduce a conformal spin-$fracn2$ gauge field $h_{(n)}=h_{alph{a}_{1}dotsalph{a}_n}$ (with $n$ spinor indices) of dimension $(2-n/2)$ and argue that it possesses a Weyl primary descendant $C_{(n)}$ of dimension $(1+n/2)$. The latter proves to be divergenceless and gauge invariant in any conformally flat space. Primary fields $C_{(3)}$ and $C_{(4)}$ coincide with the linearised Cottino and Cotton tensors, respectively. Associated with $C_{(n)}$ is a Chern-Simons-type action that is both Weyl and gauge invariant in any conformally flat space. These actions, which for $n=3$ and $n=4$ coincide with the linearised actions for conformal gravitino and conformal gravity, respectively, are used to construct gauge-invariant models for massive higher-spin fields in Minkowski and anti-de Sitter space. In the former case, the higher-derivative equations of motion are shown to be equivalent to those first-order equations which describe the irreducible unitary massive spin-$fracn2$ representations of the 3D Poincar'e group. Finally, we develop $calN=1$ supersymmetric extensions of the above results.

Full work available at URL: https://arxiv.org/abs/1806.06643

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