Non perturbative structure of quantum gravity and superstring theory

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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