Non-perturbative Study of (Super) String Theory by Means of Conformal Field Theory

点击翻译按钮获取中文摘要

In 1989 some important results were obtained from the study of the fundamental problems of conformal field theory. A general method was found to construct super-primary fields with integer or half-integer spins by Sasaki et al., who also showed that it is impossible to construct the spin-3 super-W-algebra proposed by Fadeev et al..Kubo et al., found fundamental properties of the Krichever-Novikov algebras and the Kac- Moody algebras on a torus. Some new insights into the anomaly inherent in a BRS currents in string theory were gained by Fujikawa et al.. They also found that string theory is indeed quantizable without restricting space-time dimensions to 26. Uehara et al., studied chaotic properties of a motion of strings on super-Riemann surfaces.In 1990 Kubo et al., formulated quantum string field theory on higher-genus Riemann surfaces on the basis of the K-N algebras. Sasaki et al., investigated the Toda lattice-field theory and obtained some interesting results. Our research results are expected to give considerable contribution to future development of conformal field theory.Workshop on 'Beyond Riemann Surfaces' was held from Feb.6 to Feb. 8 at Research Institute for Theoretical Physics, Hiroshima University, where we discussed new problems on topological field theory, soluvable models, link polynomials, global structure of conformal field theory, low dimensional topology, K-N algebras, Kac-Moody Lie groups, fundamental groups and the Laplacian and 3 dimensional gravity. The aim of the workshop is to find some more promising theories than conformal field theory.