Real formulations of complex gravity and a complex formulation of real gravity

Peter Peldán
1994 Nuclear Physics B  
Two gauge and diffeomorphism invariant theories on the Yang-Mills phase space are studied. They are based on the Lie-algebras so(1,3) and so(3) -- the loop-algebra of so(3). Although the theories are manifestly real, they can both be reformulated to show that they describe complex gravity and an infinite number of copies of complex gravity, respectively. The connection to real gravity is given. For these theories, the reality conditions in the conventional Ashtekar formulation are represented by normal constraint-like terms.
doi:10.1016/0550-3213(94)00379-3 fatcat:vqzgpcg5vvdmhhplhf3u4tzuwa