Dr. Concha-Aguilera, Patrick

In this paper, we present and classify the supersymmetric extensions of extended kinematical algebras, at the basis of non-Lorentzian physics theories. The diverse kinematical superalgebras are here derived by applying non- and ultra-relativistic expansion procedures involving different semigroups. We then build three-dimensional Chern-Simons non-Lorentzian supergravity theories based on such (extended) kinematical superalgebras, providing the supersymmetry transformation laws of the fields and the field equations of the models, which correspond to the vanishing of the curvature two-forms. In fact, the expansion procedure adopted allows to automatically end up with a non-degenerate bilinear invariant trace for the (extended) kinematical superalgebras. The latter is a crucial ingredient of the Chern-Simons field-theoretical formulation, as it allows to include a kinetic term for each gauge field of the theory, implying the vanishing of the curvature two-forms as field equations.

In this work we present a non-relativistic gravity theory defined in four spacetime dimensions using the MacDowell-Mansouri geometrical formulation. We obtain a Newtonian gravity action which is constructed from the curvature of a Newton-Hooke version of the so-called Newtonian algebra. We show that the non-relativistic gravity theory presented here contains the Poisson equation in presence of a cosmological constant. Moreover we make contact with the Modified Newtonian Dynamics (MOND) approach for gravity by considering a particular ansatz for a given gauge field. We extend our results to a generalized non-relativistic MacDowell-Mansouri gravity theory by considering a generalized Newton-Hooke algebra.