Abstract
Renormalization group techniques are used in order to obtain the improved nonlocal gravitational effective action corresponding to any asymptotically free GUT, up to invariants which are quadratic on the curvature. The corresponding nonlocal gravitational equations are written down, both for the case of asymptotically free GUTs and also for quantum R2-gravity. The implications of the results when obtaining the flux of vacuum radiation through the future null infinity are briefly discussed.
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