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  4. Three-dimensional hypergravity theories and semigroup expansion method
 
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Three-dimensional hypergravity theories and semigroup expansion method
Dr. Concha-Aguilera, Patrick 
Facultad de Ingeniería
Dra. Rodríguez-Durán, Evelyn 
Facultad de Ingeniería
Caroca, Ricardo
Matulich, Javier
Tempo, David
10.1007/JHEP08(2023)215
Springer Nature
2023
In this work, we apply the semigroup expansion method of Lie algebras to construct novel and known three-dimensional hyper-gravity theories. We show that the expansion procedure considered here yields a consistent way of coupling different three-dimensional Chern-Simons gravity theories with massless spin- 5/2 gauge fields. First, by expanding the osp (1|4) superalgebra with a particular semigroup a generalized hyper-Poincaré algebra is found. Interestingly, the hyper-Poincaré and hyper-Maxwell algebras appear as subalgebras of this generalized hyper-symmetry algebra. Then, we show that the generalized hyper-Poincaré CS gravity action can be written as a sum of diverse hyper-gravity 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 Inönü-Wigner contraction which can be seen as a generalization of the existing vanishing cosmological constant limit between the hyper-AdS and hyper-Poincaré gravity theories.
Chern-Simons theories
Higher spin symmetry
Higher spin gravity
Supergravity models
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