Preface

Abstract

Almost a century has gone by since the discovery of general relativity and quantum mechanics, yet the goal of finding a consistent theory of quantum gravity nonetheless remains elusive. After the two major triumphs of modern quantum field theory, quantum electrodynamics and the quantization of non-abelian gauge theories (including quantum chromodynamics and the electro-weak theory) the early seventies provided high hopes that a quantum treatment of general relativity might be around the corner. However, to the dismay of many, the results of t’ Hooft and Veltman conclusively established that quantum gravity is not perturbatively renormalizable, thus confirming earlier suspicions based on purely dimensional arguments. Disturbingly, the divergences which appear in gravity at one loop order in the semiclassical expansion, involving curvature squared terms, cannot be re-absorbed into a redefinition of the coupling constants, thereby making it difficult to derive unambiguous statements about the properties of the underlying quantum theory. More importantly, the now exhaustively explored examples of quantum electrodynamics and non-abelian gauge theories have established that until these ultraviolet renormalization effects are consistently and systematically brought under control, it will be very difficult to make any sort of physically relevant predictions. To this day, the ultraviolet problems of quantum gravity border on the speculative for many: after all, if quantum gravity effects are relevant at distances of the order of the Planck length (10−33cm), then these might very well have little relevance for laboratory particle physics in the foreseeable future. But how could one so conclude without actually doing the relevant calculations? What if new, non-perturbative scales arise in the renormalization procedure, as occurs in non-abelian gauge theories? Since the seventies, strategies that deal with the problem of ultraviolet divergences in quantum gravity have themselves diverged. Some have advocated the search for a new theory of quantum gravity, a theory which does not suffer from ultraviolet infinity problems. In supersymmetric theories, such as supergravity and ten-dimensional superstrings, new and yet unobserved particles are introduced thus reducing the divergence properties of Feynman amplitudes. In other, very restricted classes of supergravity theories in four dimensions, proponents have claimed that