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arXiv · 2208.01013

Non-relativistic and Ultra-relativistic Expansions of Three-dimensional Spin-3 Gravity Theories

Patrick Concha·Carla Henríquez-Báez·Evelyn Rodríguez
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Abstract

In this paper, we present novel and known non-relativistic and ultra-relativistic spin-3 algebras, by considering the Lie algebra expansion method. We start by applying the expansion procedure using different semigroups to the spin-3 extension of the AdS algebra, leading to spin-3 extensions of known non-relativistic and ultra-relativistic algebras. We then generalize the procedure considering an infinite-dimensional semigroup, which allows to obtain a spin-3 extension of two new infinite families of the Newton-Hooke type and AdS-Carroll type. We also present the construction of the gravity theories based on the aforementioned algebras. In particular, the expansion method based on semigroups also allows to derive the (non-degenerate) invariant bilinear forms, ensuring the proper construction of the Chern-Simons gravity actions. Interestingly, in the vanishing cosmological constant limit we recover the spin-3 extensions of the infinite-dimensional Galilean and infinite-dimensional Carroll gravity theories.

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Patrick Concha, Carla Henríquez-Báez, Evelyn Rodríguez. 2022-10-12. Non-relativistic and Ultra-relativistic Expansions of Three-dimensional Spin-3 Gravity Theories. https://doi.org/10.1007/jhep10(2022)155

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