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

1989年，在对共形场论基本问题的研究中获得了一些重要的结果。Sasaki等人发现了一种构造整数或半整数自旋的超初级场的一般方法，他也证明了Fadeev等人提出的自旋为3的超w代数是不可能构造的。Kubo等人在环面上发现了krichhever - novikov代数和Kac- Moody代数的基本性质。Fujikawa等人对弦理论中BRS电流固有的异常现象有了一些新的认识。他们还发现，弦理论确实可以在不限制时空维度为26的情况下量子化。Uehara等人研究了超黎曼曲面上弦运动的混沌性质。1990年Kubo等人在K-N代数的基础上，在高格黎曼曲面上建立了量子弦场论。Sasaki等人研究了Toda格场理论，得到了一些有趣的结果。我们的研究成果有望对未来共形场理论的发展做出重大贡献。“超越黎曼曲面”研讨会于2月6日至2月8日在广岛大学理论物理研究所举行，我们讨论了拓扑场论、可解模型、连接多项式、共形场论的整体结构、低维拓扑、K-N代数、Kac-Moody李群、基本群、拉普拉斯和三维引力等新问题。研讨会的目的是寻找一些比共形场理论更有前途的理论。

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.