Quantum study of ground state and black holes in superstring theories

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This research project achieved the following results.(1) It is important to study noncommutative theories realized on branes in string theories in order to gain deep understanding of quantum gravity. We have studied theories with noncommutativity not only between space and space coordinates but also space and time, and have given foundation to the nonperturbative analysis of these theories. Furthermore we explicitly examined the transformation properties of 3-dimensional theories under duality. We have also studied supersymmetry and fluctuation spectrum around D-branes realized as solitonic solutions in these theories. As an extention of this work, we showed that there is unbroken supersymmetry in D and anti-D-brane system if we have nontrivial backgrounds. The moduli space of solitons is also clarified and the results are used to examine their scatterings.(2) Time-dependent solutions are important to study formation of black holes and cosmology in terms of string theory. When we consider D-branes in such space-time, we showed that field theories and/or open string theories are realized on the branes. We have also given most general time-dependent brane solutions. They are exact solutions with time-dependent size of the internal space, and it turns out that they give very interesting cosmological models with inflation. They give very promising models to explain the present expanding universe with acceleration and attract much, attention.(3) PP wave space-time is known to give solvable background of string theory, and hence is very interesting background. We studied this geometry focusing on the supersymmetry aspects of the solution. Also systematic method is developed to derive various forms of p-brane ((p+1)-dimensional) action, and we plan to use the result to study quantization of p-branes.