Free Nonperturbative effects in quantum gravity and string theory

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It is important to make constructive definitions of quantum gravity and the string thory in such a way that various physical quantities can be obtained at least by nemerical calaulations. As basic steps in this direction we performed the following projects :1.In order to construct a local field theory which represeuts the string theory, we proved numerically that the complex structure can be introdnced on a discretized worldsheet comesponding to C*1 matrix models.2.We developed a systeratic method for epsilon-expansion in 2+epsilon dimensional quantum gravity.3.The string field theory was developed further and formulated in a back-ground indeperdent way.4.The short distance behavor of space-time fluctuations was investigated by considering on operator product expansion in quantum gravity.