Study of Non-Perturbative Dynamics of Superstring Theory through Supersymmetric Yang-Mills Theory

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The main aim of the present research project has been to understand the non-perturbative properties of superstring theory and to give its basic formulation through the analysis of various aspects of supersymmetric Yang-Mills theory. We have obtained rather satisfactory results concerning the analysis of soliton solutions in non-commutative super Yang-Mills theory and its brane interpretation, though there still remains much to be clarified in other planned subjects. However, we have accomplished remarkable results in the analysis of tachyon condensation using String Field Theory, which is a subject not contained in the original plan. The following is a concrete description of our researches in the years 2000-2002:1) Analysis of monopole solution in non-commutative super Yang-Mills theory: We have presented, to second order in the non-commutativity parameter θ, the monopole solution to non-commutative super Yang-Mills theory, and given a brane interpretation to the solution.2) Analysis of tachyon condensation using string field theory: We have shown that the classical solution of string field theory representing the vacuum with tachyon condensation (tachyon vacuum) satisfies, besides the equation of motion, another important requirement of BRST invariance. We have also carried out an analysis of fluctuation around the solution to and obtained results which strongly support the expectation that there is no physical open string states around the tachyon vacuum.3) Study of Vacuum String Field Theory: We have carried out pioneering studies on the problem of whether Vacuum String Field Theory (VSFT), which is a candidate string field theory expanded around the tachyon vacuum, can be related to ordinary open string theory. We have constructed a classical solution representing the perturbative vacuum, analyzed the fluctuation spectra around the solution, and so on, and obtained results supporting the expectation.