Analysis of algebraic and geometrical structure in superstring theory

在这个项目中，首席研究员S.Uehara研究了超膜理论，这是M理论的重要基础激发之一。上原成功地给出了仿射李代数的矩阵表示，当超膜包裹在一个圆上时，仿射李代数就出现了。Uehara还给出了包裹超膜在2-环面上的矩阵表示。此外，Uehara成功地直接从超膜作用量导出了(p，q)弦作用量。S.青山用流形的度规给出了四元Kaehler流形的三重态Killen势的新公式。青山还研究了一阶形式的Kaehler模型上的二维非线性Sigma模型，并用Berkovits方法构造了G对称流和基数。T.Kawai讨论了D2-D0膜的几何结构可能与Calabi-Yau三重的Gromov-Witten理论有关。河井还讨论了与Gopakumar-Vafa不变量的关系。H.Awata研究了欧米茄背景中的Nekrasov配分函数与D膜的模空间之间的联系，并证明了由Nekrasov公式得到的自旋含量与局部Hirzebruch面上的Gopakumar-Vafa不变量是一致的。Awata还根据Macdonald函数的专门化提出了精化拓扑点。

In this project, the head investigator S. Uehara investigated the supermembrane theory which is one of the important fundamental excitations of M-theory. Uehara succeeded in giving the matrix representation of the affine Lie algebra which appears when supermembrane wraps on a circle. Uehara also gave the matrix representation of the wrapped supermembrane on 2-torus. Furthermore, Uehara succeeded in deriving the(p, q)-string action directly from the supermembrane action.S. Aoyama showed a new formula of the triplet Killing potentials of quatenionic Kaehler manifolds with the metric of the manifolds. Aoyama also investigated two-dimensional non-linear sigma-models on the Kaehler maniforld G/H in the first order formalism and constructed the G-symmetry currents and primaries by using the Berkovits method.T. Kawai discussed the geometry of D2-D0 branes may be related to Gromov-Witten theory of Calabi-Yau threefolds. Kawai also discussed the relation to Gopakumar-Vafa invariants.H. Awata investigated the connection of Nekrasov's partition function in the Omega background and the moduli space of D-branes and showed that the spin contents obtained by Nekrasov's formula are consistent with the Gopakumar-Vafa invariants on a local Hirzebruch surface. Awata also proposed the refined topological vertex in terms of the specialization of the Macdonald function.