Resummation and Higher Order Renormalization in 4D Quantum Gravity

Higher order renormalization in 4D quantum gravity is carried out using dimensional regularization with great care concerning the conformal-mode dependence. In this regularization, resummation can be automatically performed without making any assumption, like done by David-Distler-Kawai. In this paper we consider a model of 4D quantum gravity coupled to QED. The renormalizability is directly checked up to O(er) and O(tr), where er and tr are running coupling constants of QED and the traceless gravitational mode. There is no other running coupling constant in our model. The conformal mode is treated exactly, which means unrenormalized. Hathrell’s results are correctly included in our computations. As a by-product, it is found that a higher order gravitational correction to the beta function of QED is negative. An advantage of our model is that at the very high-energy region it has a close resemblance to exactly solvable 2D quantum gravity. Thus, we can argue physical states of 4D quantum gravity at this region in parallel with those of 2D quantum gravity, which may be described by diffeomorphism invariant composite fields. E-mail address : [email protected]