Three-dimensional hypergravity theories and semigroup expansion method

DOI10.1007/JHEP08(2023)215arXiv2304.10624MaRDI QIDQ6074274

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Publication date: 12 October 2023

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Abstract: In this work we present novel and known three-dimensional hypergravity theories which are obtained by applying the powerful semigroup expansion method. We show that the expansion procedure considered here yields a consistent way of coupling different three-dimensional Chern-Simons gravity theories with massless spin-$frac52$ gauge fields. First, by expanding the $mathfrakospleft(1|4ight)$ superalgebra with a particular semigroup a generalized hyper-Poincar'e algebra is found. Interestingly, the hyper-Poincar'e and hyper-Maxwell algebras appear as subalgebras of this generalized hypersymmetry algebra. Then, we show that the generalized hyper-Poincar'e CS gravity action can be written as a sum of diverse hypergravity CS Lagrangians. We extend our study to a generalized hyper-AdS gravity theory by considering a different semigroup. Both generalized hyperalgebras are then found to be related through an In"on"u-Wigner contraction which can be seen as a generalization of the existing vanishing cosmological constant limit between the hyper-AdS and hyper-Poincar'e gravity theories.

Full work available at URL: https://arxiv.org/abs/2304.10624

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