Extended Kinematical 3D Gravity Theories

Abstract

In this work, we classify all extended and generalized kinematical Lie algebras that can be obtained by expanding the $\mathfrak{so}\left(2,2\right)$ algebra. We show that the Lie algebra expansion method based on semigroups reproduces not only the original kinematical algebras but also a family of non- and ultra-relativistic algebras. Remarkably, the extended kinematical algebras obtained as sequential expansions of the AdS algebra are characterized by a non-degenerate bilinear invariant form, ensuring the construction of a well-defined Chern-Simons gravity action in three spacetime dimensions. Contrary to the contraction process, the degeneracy of the non-Lorentzian theories is avoided without extending the relativistic algebra but considering a bigger semigroup. Using the properties of the expansion procedure, we show that our construction also applies at the level of the Chern-Simons action.

arXiv comment31 pages, 5 figures, revised version accepted in JHEP

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Cited by in corpus (7)

• Quantization of Carrollian fermions
• Non-Lorentzian Supergravity and Kinematical Superalgebras
• AdS${}_3$ Carroll gravity: asymptotic symmetries and C-thermal configurations
• Three-dimensional non-relativistic Hietarinta supergravity
• Four dimensional topological supergravities from transgression field theory
• Extended Bargmann FDA and non-relativistic gravity
• Boson-fermion algebraic mapping in second quantization