Constructive Definition of String Theory and Unified Theory of Elementary Particles

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A constructive formulation of string theory is proposed and analyzed. More concretely,(1)We have analyzed the structure of IIB matrix model both in analytic and numerical methods, and examined whether the dimension of the space-time and the field contents of the standard model are properly generated by this model.(2)We also have analyzed how curved space-time can be represented by the matrix model. We have shown that the fundamental symmetries of the general relativity, diffeomorphisms and local Lorentz symmetry, are included in the matrix model as a part of the SU(N) symmetry of the matrices. We have further shown that the path integral of the matrix model contains all possible manifolds with dimensions less than or equal to ten. In this sense, the matrix model describes not only the fluctuating metric on a given manifold but also all possible topologies of space-time.(3)We have generalized the above analysis to the case of supergravity, and proposed a new type of matrix model in which the symmetry of supergravity is manifest. We are investigating whether this model is equivalent to the original IIB matrix model or not.(4)We have performed a higher order calculation of the improved mean field approximation, and shown that the four dimensional space-time is most plausible as the ground state of IIB matrix model.By combining the obtained results, we are trying to reveal the fundamental symmetry and principles of string theory, and find the ultimate constructive definition of the theory of everything.