Quantum Gravity

9STRING THEORY9.1 General introductionThe approaches discussed so far start from the assumption that the gravitationalfield can be quantized separately. That this can really be done is, however, notclear. One could imagine that the problem of quantum gravity can only be solvedwithin a unified quantum framework of all interactions. The only serious candidateup to now to achieve this goal is superstring theory. Our interest here ismainly to exhibit the role of quantum gravitational aspects. It is not our aim togive an introduction into the many physical and mathematical aspects of stringtheory. This is done in a series of excellent textbooks; see in particular Greenet al. (1987), Lüst and Theisen (1989), Polchinski (1998a,b), Kaku (1999), andZwiebach (2004). Mohaupt (2003) gives a concise overview with particular emphasison gravitational aspects. For more details we refer the reader to thesereferences.String theory started as an attempt to explain the spectrum of hadrons. Afterthe discovery of quantum chromodynamics and its successful predictions, it wasabandoned as such. It was, however, realized that string theory could in principleimplement a theory of quantum gravity (Scherk and Schwarz 1974; Yoneya 1974).The main reason is the appearance of a massless spin-2 particle in the spectrumof the string. As we have learned in Chapter 2, such a particle necessarily leadsto GR in the low-energy limit.String theory transcends the level of local field theory because its fundamentalobjects are one-dimensional entities (‘strings’) instead of fields defined at space–time points. More recently it has turned out that higher-dimensional objects(‘branes’) appear within string theory in a natural way and on an equal footingwith strings (see below). We shall nevertheless continue to talk about ‘stringtheory’.What are the main features of string theory?1. String theory necessarily contains gravity. The graviton appears as an excitationof closed strings. Open strings do not contain the graviton bythemselves, but since they contain closed strings as virtual contributions,the appearance of the graviton is unavoidable there, too.2. String theory necessarily leads to gauge theories since the correspondinggauge bosons are found in the string spectrum.3. String theory seems to need supersymmetry (SUSY) for a consistent formulation.Fermions are therefore an essential ingredient.279