Abstract
We obtain the effective action of four-dimensional quantum gravity, induced by N massless matter fields, by integrating the renormalization group (RG) flow of the relative effective average action. By considering the leading approximation in the large N limit, where one neglects the gravitational contributions with respect to the matter contributions, we show how different aspects of quantum gravity, such as asymptotic safety, quantum corrections to the Newtonian potential and the conformal anomaly-induced effective action, are all represented by different terms of the effective action when this is expanded in powers of the curvature.
Highlights
Even if we are still lacking a quantum theory of gravitational phenomena we are starting to accumulate interesting partial results which will probably be important bits of the final theory
As a first step toward understanding the gravitational effective action we studied the effective action induced by massless matter fields interacting solely with the background geometry
We proposed an expansion of the effective action in powers of the curvatures and we showed how various known results about quantum gravity could be seen as arising from different terms of it
Summary
Even if we are still lacking a quantum theory of gravitational phenomena we are starting to accumulate interesting partial results which will probably be important bits of the final theory. These are, among others, the conformal anomaly induced effective action, which was first written down in [1]; the low energy corrections to the Newtonian gravitational potential analyzed in [2]; the possible ultraviolet (UV) finite completion of the theory described in the asymptotic safety scenario [3]. We will extend the large N analysis to a non-local truncation of effective average action where this is expanded in powers of the curvature
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