Non-relativistic spin-3 symmetries in 2+1 dimensions from expanded/extended Nappi-Witten algebras

Abstract

We show that infinite families of non-relativistic spin-$3$ symmetries in $2+1$ dimensions, which include higher-spin extensions of the Bargmann, Newton-Hooke, non-relativistic Maxwell, and non-relativistic AdS-Lorentz algebras, can be obtained as Lie algebra expansions of two different spin-$3$ extensions of the Nappi-Witten symmetry. These higher-spin Nappi-Witten algebras, in turn, are obtained by means of Inönü-Wigner contractions applied to suitable direct product extensions of $\mathfrak{sl}(3,\mathbb{R})$. Conversely, we show that the same result can be obtained by considering contractions of expanded $\mathfrak{sl}(3,\mathbb{R})$ algebras. The method can be used to define non-relativistic higher-spin Chern-Simon gravity theories in $2+1$ dimensions in a systematic way.

arXiv comment44 pages, typos corrected, references added

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Cited by in corpus (6)

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• Asymptotic structure of three-dimensional Maxwell Chern-Simons gravity coupled to spin-3 fields
• Three-dimensional non-relativistic Hietarinta supergravity
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