Towards nonperturbative M-theory

本研究项目的主要目标是进行各种研究，以具体构建所谓的M理论的非微扰公式。M理论被认为是超弦理论背后的一个更深层次的理论，自从它被首次发现以来，人们已经研究了30多年，作为统一基础物理学两个主要框架的主要候选者，即量子理论和相对论。在这个项目中，我们发展了各种新的方法来表述弦理论及其向M理论的可能扩展。我们还发现了弦理论在短程区时空结构方面的各种新性质，特别是对称性，如超对称性、共形对称性、全息原理和时空不确定性原理，并详细讨论了D-膜自由度和超膜的动力学性质。这被认为是弦/M理论的主要物理自由度。

The main objective of this research project is to carry out various studies towards a concrete construction of nonperturbative formulation of the so-called M-theory. The M-theory is supposed to be a deeper theory behind superstring theory, which has been studied more than 30 years since its first discovery as a prime candidate for unifying two principal frameworks of fundamental physics, namely, quantum theory and relativity theory. In this project, we have developed various new methods for formulating string theories and their possible extensions towards M-theories. We have also found various new properties of string theories with respect to its space-time structure in the short-distance regime, and in particular, to symmetry properties, such as supersymmetry, conformal symmetry, holographic principle and space-time uncertanty principle.We have also discussed detailed dynamics of the D-brane degrees of freedom and supermembranes, which have been expected to be prime physical degrees of freedom of string/M-theories.