One-loop dynamics of four-dimensional string theory

The report discusses the dynamical aspects of four-dimensional string theory as compared with the field theory. These investigations are important to connect the string theory with phenomena in the energy scale concerned. One of the severest difficulties in string theory is the fact that the string theory is formulated in the critical dimensions, namely 10 and 26 for superstring and bosonic string, respectively. Some problems in four-dimensional superstring theory and the answers obtained are summarized. The answers are as follows. It is possible to obtain renormalization group equations (RGEs). For the RGEs of supersymmetric (N=1) theory, beta functions are shown to be the same as those of the corresponding field theory. As for the model investigated here (N=1 supersymmetric orbifold compactification of heterotic string), the structures of internal spaces appear in two ways. The structure of six-dimensional orbifold is reflected in amplitudes through the zero modes of one-loop propagators of the twisted fields and that of sixteen-dimensional internal space through the indices of the representations to which massless states of the theory belong. It is possible to investigate symmetry breakings. One can encounter Fayet-Illiopoulis model like situations in supersymmetric models. One can obtain one-loop effective potential of massless scalar bosons and discuss the possibilities of symmetry breakings. (Nogami, K.)