Constructive Formulation of String Theory

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A constructive formulation of string theory is proposed and analyzed. We have expressed string theory in terms of a matrix model called IIB matrix model (or sometimes called IKKT model), and examined whether the dimension of the space-time and the field contents of the standard model are properly generated by this model. We also have analyzed the relation between IIB matrix model and the non-commutative geometry, and found a mechanism of realizing curved space-time and the general coordinate invariance in this model. Although we need an intensive numerical simulation or some new analytic method to prove the validity of our formalism, we expect that this model will explain various physical quantities such as masses of quarks and leptons, and serves as the theory of everything.