Nonperturbative Study of Quantum Gravity and String Theories

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The superstring theory is one of the most promising candidates for unified theory of the 4 kind of the fundamental interactions in Nature : strong force, weak force, electromagnetic force and gravitational force. It is one of the most interesting problems to investigate the properties of elementary particles and the birth of the universe by completing the superstring theory. Recently there has been a lot of development to construct it nonperturbatively. Among those a formulation in terms of "D brane" which is solitonic excitation and the duality method become important and then a kind of the master theory called M theory has been intensively investigated.However these nonperturbative string theories do not describe creation and annihilation and thus they have not yet come to 2nd quantized string field theory. Then I have been working, with Professor Holger B.Nielsen, the Niels Bohr Institute, Denmark, on constructing string field theory by using the right- and left- moving modes as constituents. In this approach it becomes apparent that we need a new symmetry analogous to the Bose statistics in bosonic particles. By using this symmetry states are formed. We are now working to derive the scattering amplitudes and check whether the duality holds.During the course of studying our string field theory we found the method how to construct the negative energy sea (Dirac sea) for bosonic particles which enables to treat the bosons similar to fermions when second quantizing. Our theory may give a solution to the long standing problem of negative energy states in bosons in quantum field theory.In quantum gravity we considered the gravity in the 2+εdimensional theory near two dimensions by means of the renormalization group and statistical field theory. By studying short distance behavior in detail we obtained scaling law and critical exponents.