Non-Perturbative Structure of Quantum Field Theories Including Quantum Gravity

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1 Quantum gravity in lower spacetime dimensions For the purpose of grasping some aspects of quantum gravity, we have analyzed higher-derivative and scalar-tensor type models in two-dimensional spacetime. We have derived WKB wave functionals and conformal anomalies using the algebra of constraint operators. In particular, we have exhibited a possibility of vanishing cosmological constant without a need of fine tuning.2 (Super) string theories as a theory of quantum gravity Through earlier works by the present head investigator and others, it has long been known that the conformally invariant relativistic string theories naturally contain Einstein's general relativity as a low energy limit. In spite of many important works in recent yeres, however, no real progress toward geometrical and nonperturbative formulations of the theory have been made. In view of this situation, we have made the following investigations. (1) Studies in the framework of light-cone string field theory; we have sh … More own that the light-cone action has a symmetry under a restricted class of general coordinate transformations. We have also shown that a redefinition of the string field corresponging to the change of the vacuum expectation value of the dilaton field induces a continuous change of the string coupling constant. This made possible to understand, on the basis of an action priciple, the fact that there is only one continuously variable constant which characterizes the string theories. (2) Preliminary studies toward background independent formulation;based on the results of the studies (1), we have proposed a possible way of formulating string field theories in a way which is independent of background spacetime metric. This proposal has since been developed further by other groups. (3) Studies of the ultraviolet structure of string theories; the string theories do not contain ultraviolet divergences because of the duality property, which perhaps implies that the concept of spacetime geometry in string theory may be radically different from the Riemannian geometry. We have proposed to interpret the duality property by assuming a new kind of uncertainty principle in spacetime. With a hope that our proposals may be useful clues, we will continue further to explore various new possibilities toward the formulation of string geometry. Less