Pseudo-orthogonal Yang-Mills theories and connections to gravity

Abstract: We formulate gauge theories on noncompact Lorentzian manifolds. For definiteness we choose an SO(1,4) gauge theory -- the isometry group of the five dimensional Minkowski space. We make use of the natural inner product to construct the Yang-Mills gauge action on four dimensional spacetime, on which the natural tetrad and metric are induced, thus breaking the symmetry to that of general relativity. In the low energy limit -- if a suitable gauge field condensate develops -- the theory reduces to the Cartan-Einstein gravity, which harbors nondynamical torsion, and is consistent with all observations. We also discuss how to couple our gauge theory of gravity to scalar and vector matter. The Hamiltonian analysis shows that the theory possesses no Ostrogradsky instabilities, however it harbors a kinetic instability. We conjecture that such a kinetic instability can be removed either by generalizing the theory to the nonlinear Born-Infeld theory, or by constraining the kinetic instability. This work is an attempt to formulate gravity as a unitary, renormalizable gauge theory without instabilities, in which the fundamental propagating degrees of freedom are in the spin-one tetrad connection.