Dr. Concha-Aguilera, Patrick

In this work we analyze the asymptotic symmetries of the three-dimensional Chern-Simons (CS) gravity theory for a higher spin extension of the so-called Maxwell algebra. We propose a generalized set of asymptotic boundary conditions for the aforementioned flat gravity theory and we show that the corresponding charge algebra defines a higher-spin extension of the max-bms3 algebra, which in turn corresponds the asymptotic symmetries of the Maxwell CS gravity. We also show that the hs3max-bms3 algebra can alternatively be obtained as a vanishing cosmological constant limit of three copies of the algebra, with three independent central charges.

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.