Lunch Seminar Patricio Salgado-Rebolledo, Pontificia Universidad Católica de Valparaíso

Abstract: We introduce an infinite-dimensional space, whose isometries are given by an infinite expansion of the Poincaré algebra. Different truncations of this symmetry define a family of extensions of the Galilei algebra. Particle actions invariant under these extended Galilean symmetries naturally lead to post-Galilean corrections in the non-relativistic limit. In the context of gravity, we construct a Chern-Simons action invariant under this infinite-dimensional algebra, which leads to a sequence of non-relativistic gravity actions that include extended Bargmann gravity and Newtonian gravity as its simplest examples. Similarly, one can define Carrollian expansions and the corresponding Chern-Simons gravity actions. The procedure can be generalized to the AdS case, from which it is possible to derive the anstaz for the large c expansion of the metric that has been recently used in the literature in the context of Newtonian gravity. Finally, we discuss how to obtain some of these extended Galilean symmetries as contractions of relativistic symmetries.