Three-dimensional (higher-spin) gravities with extended Schrödinger and \(l\)-conformal Galilean symmetries

DOI10.1007/JHEP07(2019)156zbMATH Open1418.83037arXiv1905.13154OpenAlexW2964891451MaRDI QIDQ2317811

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Publication date: 12 August 2019

Published in: (Search for Journal in Brave)

Abstract: We show that an extended $3D$ Schr"odinger algebra introduced in [1] can be reformulated as a $3D$ Poincar'e algebra extended with an SO(2) R-symmetry generator and an $SO(2)$ doublet of bosonic spin-1/2 generators whose commutator closes on $3D$ translations and a central element. As such, a non-relativistic Chern-Simons theory based on the extended Schr"odinger algebra studied in [1] can be reinterpreted as a relativistic Chern-Simons theory. The latter can be obtained by a contraction of the $SU(1,2)imesSU(1,2)$ Chern-Simons theory with a non principal embedding of $SL(2,mathbbR)$ into $SU(1,2)$. The non-relativisic Schr"odinger gravity of [1] and its extended Poincar'e gravity counterpart are obtained by choosing different asymptotic (boundary) conditions in the Chern-Simons theory. We also consider extensions of a class of so-called $l$-conformal Galilean algebras, which includes the Schr"odinger algebra as its member with $l=1/2$, and construct Chern-Simons higher-spin gravities based on these algebras.

Full work available at URL: https://arxiv.org/abs/1905.13154

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