Studies in Matrix Model and Spacetime Structure

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Superstring theory is a candidate for the unified theory including gravity in particle physics, the theory where we can study spacetime and matter at the same footing. Based on the matrix models which are a nonperturbative definition of superstring theory, we study the spacetime structure and the matter realization on it. The main results that we have obtained during the term of this grant are summarized in the following three categories.1. We studied the relation between the spacetime structure in the matrix model and that in the supergravity theory. By investigating the Wilson loop operator in the matrix model, we constructed systematically various vertex operators that alter the background field configurations in the supergravity theory. Then, by using these vertex operators, we analyzed the condensation of the fields corresponding to the supergravity multiplets, such as the gravitational field, in the matrix model.2. We studied the chiral structure of matter in matrix model and noncommutative geometry. By applying the Ginsparg-Wilson relation developed in the lattice field theory, we gave the general prescription to define the GW Dirac operator and to formulate the topological invariant and the index in general noncommutative geometries. We constructed topologically nontrivial configurations, analyzed their dynamics, and developed the understanding of the realization mechanism of chiral fermion on our spacetime in superstring theory and matrix model.3. We found that the Hawking radiation from the black holes can be understood by using the anomaly in the field theory, which we also applied to various black holes, such as the rotating black holes and the higher dimensional black holes. These results are expected to be applied to the study of various thermodynamical quantities such as black hole entropy.