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The renormalization group (RG) properties of quantum gravity are explored,using the vielbein and the spin connection as the fundamental field variables.The scale dependent effective action is required to be invariant both underspace time diffeomorphisms and local frame rotations. The nonperturbative RGequation is solved explicitly on the truncated theory space defined by a threeparameter family of Holst-type actions which involve a running Immirziparameter. We find evidence for the existence of an asymptotically safefundamental theory, probably inequivalent to metric quantum gravity constructedin the same way.

Renormalization Group Flow of the Holst Action