TOWARDS A UNIFICATION OF GRAVITY AND YANG-MILLS THEORY

We introduce a gauge and diffeomorphism invariant theory on the Yang-Mills phase space. The theory is well defined for an arbitrary gauge group whose Lie algebra admits a nondegenerate invariant bilinear form, and it contains only first class constraints. With gauge group SO(3, C), the theory equals the Ashtekar formulation of gravity with a cosmological constant. For Lorentzian signature, the theory is complex, and we have not found any good reality conditions. In the Euclidean signature case, everything is real. By using gauge group SO(3) X G(YM) and doing a weak field expansion around de Sitter spacetime, the theory is shown to give the conventional Yang-Mills theory to the lowest order in the fields.