Spontaneously Broken Erlangen Program Offers a Bridge Between the Einstein and the Yang-Mills Theories

Abstract: We shall give dynamics to our spacetime manifold by first identifying the local affine symmetry as the characterizing symmetry for our geometry \'a la Felix Klein, and then by prescribing 16 gauge vector bosons to this symmetry \'a la Yang and Mills. The locally affine symmetric Yang-Mills Lagrangian in the presence of a background world metric, and the corresponding equations of motion, are respectively constructed and derived. Spontaneous breaking of the local affine symmetry to the local Lorentz symmetry is achieved by classical solutions to the equations of motion. In these classical solutions, the 16 gauge vector bosons are shown to select the Schwarzschild metric as one among the admissible background world metrics. Classical gravity is expressed by a spontaneously broken Erlangen program.