Abstract
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 $\mathrm{SO}(3,C)$, 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 $\mathrm{SO}(3)\ifmmode\times\else\texttimes\fi{}{G}^{\mathrm{YM}}$ 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.
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