Symmetries of string theory and dynamics of D-branes

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We briefly summarize our results reported in our papers listed below.i) Kamimura et al extended the canonical formulation for a non-commutative field proposed by Llosa and Vives and applied it to a NCFT. In their formulation, the Seiberg-Witten map can be understoodas a canonical transformation.ii) Supersymmetric algebra on a maximally supersymmetric supergravity background has been found recently. Further, th* super-pp-wave algebra has been obtained in the Penrose limit. It is also known that the superstring on this background is exactly solvable. Kamimura et al. found that the Penrose limit can be realized as an algebraic contractio and the super-pp wave algebra shows up from the super AdS_5 x S^5 in the limit.ii) It is well-known that a symmetry tends to be broken in the Wilsonian RG. The gauge symmetry is the most important and crucial case if we would like to consider a theory in the Wilsonian RG. Igarashi et al. have shown that the symmetry survives even in the presence of the IR cutoff though it is modified by the regularization.iii) The lattice gauge theory is a natural way to study the super YM theory nonperturbatively. However, a suitable formulation has not been found. In the last two papers on the list, Itoh et al. reported a presence of a Grassmann od* transformation relating fermions and link variables. The relation to the continuum supersymmetry is not yet clear and under investigation.