Investigations on closed strings and homogeneous spaces in matrix models

矩阵模型中闭弦和齐次空间的研究

• 批准号: 15540298
• 负责人: KITAZAWA Yoshihisa
• 金额: $ 1.54万
• 依托单位: High Energy Accelerator Research Organization (2004-2006)The High Energy Accelerator Research Organization (2003)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2006
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15540298/
• 关键词: superstring; matrix models; noncommutative homogeneous space; supersymmetry; Wilson line; supergravity; 時空の微視的構造; 正の宇宙項; 等質空間; 非摂動的定式化; IIB行列模型; ウイルソンライン; 非可換等質空間; 超対称性; Wilson line; 超重力理論; 非可換時空上のゲージ理論; トホーフト結合定数の同定; 4次元的時空

It is realized that spacetime may be understood microscopically in terms of D-branes which are nonperturbative degrees of freedom in superstring theory. We hope it is useful to investigate IIB matrix model from such a perspective. It is considered that the spacetime structure is determined from the distributions of the matrix eigenvalues. We may consider noncommutative homogeneous spaces as concrete examples. We can construct such spacetime in matrix models by a group theoretic method. Since they possess the positive cosmological constant just like de Sitter spacetime, we believe they are relevant to understand the structure of realistic spacetime. We can estimate the probability for a particular spacetime to be realized in IIB matrix model y evaluation the effective action for such a background. We have found that such a probability depends on the dimensionality of the spacetime in the large N limit. Furthermore we have found that it exhibits the minimum for the 4 dimensional spacetime. We believe that the Wilson line operators play an important role to understand gravity in matrix models. We have investigated the structure of the spergravity vertex operators and their correlation functions.

我们认识到，时空可以用超弦理论中的非摄动自由度的d膜在微观上理解。我们希望从这个角度来研究IIB矩阵模型是有用的。认为时空结构是由矩阵特征值的分布决定的。我们可以把非交换齐次空间作为具体的例子。我们可以用群理论方法在矩阵模型中构造这样的时空。由于它们和德西特时空一样具有正的宇宙学常数，我们认为它们与理解现实时空的结构是相关的。我们可以通过评估这种背景下的有效作用来估计特定时空在IIB矩阵模型中实现的概率。我们发现这种概率取决于大N极限下时空的维数。此外，我们还发现它在四维时空中表现出最小值。我们认为威尔逊线算子在理解矩阵模型中的重力方面起着重要的作用。研究了重力顶点算子的结构及其相关函数。

项目成果

Fuzzy Spacetime with SU(3) Isometry in the IIB Matrix Model

IIB 矩阵模型中具有 SU(3) 等距的模糊时空

• 发表时间: 2006
• 期刊: Phys. Rev. D73
• 作者: H.Kaneko;Y.Kitazawa;D.Tomino
• 通讯作者: D.Tomino

Correlators of matrix models on homogeneous Spaces

齐次空间上矩阵模型的相关器

• 发表时间: 2004
• 期刊: Nucl. Phys. B700
• 作者: Yoshihisa Kitazawa;Yastoshi Takayama;Dan Tomino
• 通讯作者: Dan Tomino

Quantum corrections on fuzzy sphere

模糊球的量子校正

• 发表时间: 2003
• 期刊: Nucl.Phys B665
• 作者: Takaaki Imai;Yoshihisa Kitazawa;Yastoshi Takayama;Dan Tomino
• 通讯作者: Dan Tomino

Graviton Propagators on Fuzzy G/H

模糊 G/H 上的引力子传播器

• 发表时间: 2006
• 期刊: JHEP 02
• 作者: Y.Kitazawa;S.Nagaoka
• 通讯作者: S.Nagaoka

Progress toward the Determination of Complete Vertex Operators for The IIB Matrix Model

IIB矩阵模型完整顶点算子确定的进展

• 发表时间: 2007
• 期刊: Phys. Rev. D75
• 作者: Yoshihisa Kitazawa;Shun'ya Mizoguchi;OsamuSaito
• 通讯作者: OsamuSaito