Analysis of algebraic and geometrical structure in superstring theory

超弦理论中的代数和几何结构分析

• 批准号: 13135212
• 负责人: UEHARA Shozo
• 金额: $ 14.59万
• 依托单位: Utsunomiya University (2006)Nagoya University (2001-2005)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research on Priority Areas
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2006
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-13135212/
• 关键词: M-theory; supermembrane; superstring; Kaehler manifolds; Calabi-Yau manifolds; Gromov-Witten invariants; Gopakumar-Vafa invariants; Nekrasov's formula; string theory; M-theory; Green-Schwarz formulation; Hirzebrush曲面; D-branes; Nekrasov's for

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.

在这个项目中，首席研究员S。Uehara研究了M理论中重要的基本激发之一的超膜理论。上原成功地给出了矩阵表示的仿射李代数出现时，超膜包裹在一个圆圈。Uehara还给出了2-torus上包裹超膜的矩阵表示。此外，上原还成功地从超膜作用量直接导出了（p，q）弦作用量。Aoyama利用四元Kaehler流形的度量给出了四元Kaehler流形的三重态Killing势的一个新公式。Aoyama还研究了Kaehler流形G/H上的二维非线性sigma模型，并利用Berkovits方法构造了G对称电流和基色。Kawai讨论了D2-D 0膜的几何可能与Gromov-Witten的Calabi-Yau三重理论有关。Kawai还讨论了与Gopakumar-Vafa不变量的关系。Awata研究了Omega背景下Nekrasov的配分函数与D-膜的模空间之间的联系，并表明由Nekrasov公式得到的自旋内容与局部Hirzebruch曲面上的Gopakumar-Vafa不变量一致。Awata还根据Macdonald函数的特化提出了精化拓扑顶点。

项目成果

More on the Triplet Killing Potentials of Quaternionic Kaehler Manifolds

有关四元凯勒流形的三重态杀伤电位的更多信息

• 发表时间: 2005
• 期刊: Physics Letters B 625・1-2
• 作者: 青山昭五

The Berkovits Method for Conformally Invariant Non-linear Sigma models on G/H

G/H 上共形不变非线性 Sigma 模型的 Berkovits 方法

• 发表时间: 2006
• 期刊: Physics Letters B 639-3. 4
• 作者: D.Amutha Rani;Y.Yamamoto;A.Saito;M.Sivakumar;Y.Tsujita;H.Yoshimizu;T.Kinoshita;S. Aoyama
• 通讯作者: S. Aoyama

(p, q)-string in the wrapped supermembrane on 2-torus

2-环面上包裹的超膜中的 (p, q)-字符串

• 发表时间: 2006
• 期刊: Physics Letters B 639-2
• 作者: H. Okagawa;S. Uehara;S. Yamada
• 通讯作者: S. Yamada

T.Kawai: "String and Vortex."Publ.RIMS. (巻号未定). (2004)

T.Kawai：“弦与涡。”Publ.RIMS（卷未定）。

S.Aoyama, T.Masuda: "The Fuzzy Algebrae of the General Kaehler Coset Space G/H【cross product】U(1)^k"Mod.Phys.Lett.. A18. 553-560 (2003)

S.Aoyama，T.Masuda：“一般凯勒陪集空间 G/H 的模糊代数【叉积】U(1)^k”Mod.Phys.Lett.. A18 (2003)。