Generalized Chern-Simons higher-spin gravity theories in three dimensions

Abstract

The coupling of spin-3 gauge fields to three-dimensional Maxwell and $AdS$-Lorentz gravity theories is presented. After showing how the usual spin-3 extensions of the $AdS$ and the Poincaré algebras in three dimensions can be obtained as expansions of $\mathfrak{sl}\left(3,\mathbb{R}\right)$ algebra, the procedure is generalized so as to define new higher-spin symmetries. Remarkably, the spin-3 extension of the Maxwell symmetry allows one to introduce a novel gravity model coupled to higher-spin topological matter with vanishing cosmological constant, which in turn corresponds to a flat limit of the $AdS$-Lorentz case. We extend our results to define two different families of higher-spin extensions of three-dimensional Einstein gravity.

version 3, 28 pages, accepted version in Nuclear Physics B

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• Non-relativistic three-dimensional supergravity theories and semigroup expansion method
• Three-dimensional exotic Newtonian gravity with cosmological constant
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• Three-dimensional Maxwellian Extended Newtonian gravity and flat limit
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• Generalized cosmological term in D=4 supergravity from a new AdS-Lorentz superalgebra
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• Non-relativistic and Ultra-relativistic Expansions of Three-dimensional Spin-3 Gravity Theories
• Three-dimensional non-relativistic supergravity and torsion
• The Maxwell group in 2+1 dimensions and its infinite-dimensional enhancements
• Hypersymmetric extensions of Maxwell Chern-Simons gravity in (2+1) dimensions
• Higher spin AdS${}_3$ gravity and Tits-Satake diagrams
• Finiteness of 3D higher spin gravity Landscape
• Symmetries of M-theory and free Lie superalgebras
• Three-dimensional Newtonian gravity with cosmological constant and torsion
• Non-relativistic spin-3 symmetries in 2+1 dimensions from expanded/extended Nappi-Witten algebras
• Resonant superalgebras and $\mathcal{N}=1$ supergravity theories in three spacetime dimensions
• Three-dimensional teleparallel Chern-Simons supergravity theory
• On Stabilization of Maxwell-BMS Algebra
• Deformation of Asymptotic Symmetry Algebras and Their Physical Realizations
• Asymptotic structure of three-dimensional Maxwell Chern-Simons gravity coupled to spin-3 fields
• Hietarinta Chern-Simons supergravity and its asymptotic structure
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• Maxwell Chern-Simons gravity in 3D: Thermodynamics of cosmological solutions and black holes with torsion
• Boson-fermion algebraic mapping in second quantization
• Generalization of extended Lie algebras by expansions of extended de Sitter algebra, in four-dimensions