Gravity from (A)dS Yang-Mills: a natural reduction

We investigate the relation between a one-parameter family of (anti)-de Sitter Yang-Mills models and Einstein-Palatini gravity in the absence of matter, realized via a In\"o\"nu-Wigner contraction of the (A)-dS algebra. The Yang-Mills action is shown to reproduce the Einstein equations of General Relativity when the parameter labelling the gauge group is set to zero. In this limit the components of the gauge connection consistently reduce to tetrads and spin connection, transforming in the standard way under the local Lorentz group. Moreover, the full gauge symmetry of the Yang-Mills action gives rise to the invariance under diffeomorphisms and local Lorentz transformations of General Relativity.