Non perturbative structure of quantum gravity and superstring theory

1. 矩阵模型和二维黑洞：Yoneya研究了与哈密顿量的特殊选择无关的一维矩阵模型的一般性质，并将二维黑洞解在共形场论方法中与弦理论的相关性质进行了比较。主要的新结果是：(1)在线性膨胀真空下线性化的速子场与黑洞背景下相应的速子场之间存在缠结变换；(2)这种类型的交织变换的存在是在矩阵模型框架内描述黑洞型背景的可能性的必要条件；(3)二维黑洞背景的弦相互作用强度与黑洞质量的平方根成反比；(4)二维黑洞的速子奇点散射振幅应该消失。这些性质在被认为描述线性膨胀真空的普通c = 1矩阵模型中是不能被满足的。Yoneya已经证明了所有这些性质都可以被满足如果一个人通过添加一个新项来修改普通的哈密顿量。在此基础上，Yoneya和A.Jevicki对变形矩阵模型进行了详细的研究，将其作为普通矩阵模型的推广的合理候选者。量子刘维尔理论：Kazama和Nicolai研究了Otto和weight最初提出的算子形式，发现了局部因果条件的新解。利用新的解，给出了关于宇宙常数的刘维尔运动方程在所有阶上的有效性的证明。二维膨胀引力：从在较低自由度的简化模型中研究量子引力的角度来看，所谓的二维膨胀引力是一个有趣的模型。然而，通常处理该模型的半经典方法对于研究诸如黑洞蒸发等重要概念问题是不满意的，因为该方法只有在物质自由度的数目(N)和黑洞质量的值较大时才有效。Kazama证明，当N = 24时，可以利用模型与中心电荷c = 24的共形不变自由场理论之间的映射来精确处理模型。此外，Kazama还展示了如何从精确的物理状态中提取描述黑洞形成的时空结构。少

1. Matrix model and two-dimensional black hole : Yoneya investigated the general properties of the one-dimensional matrix models that are independent of the special choice of the hamiltonian, comparing with the related properties of the 2D black hole solution in the conformal field theory approach to the string theory. Main new results are that (1) there exists an intertwining transformation connecting the linearized tachyon field about the linear-dilaton vacuum to the corresponding tachyon field about the black hole background ; (2) the existence of the intertwining transformation of this type is a necessary condition for the possibility of describing the black hole type background within the framework of the matrix models ; (3) the strength of string interaction about the 2D black hole background is inversely proportional to the square root of the black hole mass ; (4) the odd-point scattering amplitudes of the tachyons about the 2D black hole should vanish. These properties cannot b … More e satisfied in the ordinary c = 1 matrix model which is believed to describe the linear dilaton vacuum. Yoneya has shown that all of these properties can be satisfied if one modifies the ordinary hamiltonian by adding a new term. Based on this, Yoneya, with A.Jevicki, has presented a detailed study of the deformed matrix model as a plausible candidate for a generalization of the ordinary matrix model.2. Quantum Liouville theory : Kazama, with Nicolai, studied the operator formalism originally proposed by Otto and Weigt and found a new solution of the local causality condition. Using the new solution, the proof is given for the validity of the Liouville equation of motion to all orders with respect to the cosmological constant.3. Two-dimensional dilaton gravity : From the point of view of studying quantum gravity in a simplified model with lower degrees of freedom, one of interesting models is the so-called 2D dilaton gravity. However, usual semi-classical method of treating this model is unsatisfactory for studying important conceptual problems such as the evaporation of black hole, because the method is valid only if the number (N) of matter degrees of freedom and the value of the black hole mass are large. Kazama showed that when N = 24 the model can be exactly treated by using the map between the model and a conformal invariant free field theory with central charge c = 24. Furthermore, Kazama exhibited how to extract the space-time structure describing the formation of black hole from the exact physical states. Less