Symmetries of string theory and dynamics of D-branes

我们简要地总结了我们在下面的论文中报道的结果。i)Kamimura等人推广了Llosa和Vives提出的非对易场的正则公式，并将其应用于NCFT。在他们的公式中，Seiberg-Witten映射可以理解为正则变换。ii)最近发现了最大超对称超重力背景上的超对称代数。进一步，在Penrose极限下得到了Th~*超pp-波代数。我们还知道，这个背景上的超弦是完全可解的。Kamimura et al.发现彭罗斯极限可以实现为代数收缩，并且超pp波代数从极限中的超ADS_5×S^5出现。ii)众所周知，在威尔逊RG中，对称性往往被破坏。如果我们想要考虑威尔逊RG中的一个理论，规范对称性是最重要和最关键的情况。Igarashi等人。结果表明，即使在IR截断存在的情况下，对称性仍然存在，尽管它被正则化修正了。iii)格点规范理论是非微扰研究超YM理论的一种自然方法。然而，还没有找到合适的配方。在名单上的最后两篇论文中，Itoh等人。报道了一个与费米子和链变量相关的Grassmann od*变换的存在。与连续体超对称性的关系尚不清楚，正在研究中。

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.