Dra. Rodríguez-Durán, Evelyn

In this paper we analyze the asymptotic symmetries of the three-dimensional Chern-Simons supergravity for a supersymmetric extension of the semisimple enlargement of the Poincaré algebra, also known as AdSLorentz superalgebra, which is characterized by two fermionic generators. We propose a consistent set of asymptotic boundary conditions for the aforementioned supergravity theory, and we show that the corresponding charge algebra defines a supersymmetric extension of the semisimple enlargement of the bms3 algebra, with three independent central charges. This asymptotic symmetry algebra can alternatively be written as the direct sum of three copies of the Virasoro algebra, two of which are augmented by supersymmetry. Interestingly, we show that the flat limit of the obtained asymptotic algebra corresponds to a deformed super-bms3 algebra, being the charge algebra of the minimal Maxwell supergravity theory in three dimensions.

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.

We present a consistent way of coupling three-dimensional Maxwell-Chern-Simons gravity theory with massless spin-5/2 gauge fields. We first introduce the simplest hyper-Maxwell-Chern-Simons gravity generically containing two massless spin-2 fields coupled with a massless Majorana fermion of spin 5/2 whose novel underlying superalgebra is explicitly constructed. We then present three alternative hypersymmetric extensions of the Maxwell algebra which are shown to emerge from the Inönü-Wigner contraction procedure of precise combinations of the ospð1j4Þ and the spð4Þ algebras. This allows us to construct distinct types of hyper-Maxwell-Chern-Simons theories that extend to include generically interacting nonpropagating spin-4 fields accompanied by one or two spin-5/2 gauge fields.