Three-dimensional hypergravity theories and semigroup expansion method

Abstract

In this work, we apply the semigroup expansion method of Lie algebras to construct novel and known three-dimensional hypergravity 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-$$ \frac{5}{2} $$ 5 2 gauge fields. First, by expanding the $$ \mathfrak{osp} $$ 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 hypersymmetry algebra. Then, we show that the generalized hyper-Poincaré 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 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.