World-sheet instanton and string duality

世界表瞬子和弦对偶性

基本信息

批准号：
10640253
负责人：
EGUCHI Tohru
金额：
$ 0.96万
依托单位：
The University of Tokyo
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 1999
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10640253/
关键词：
Superstring theory σ model Calabi-Yau string theory modular invariance A-D-E classification topological string theory instanton virasoro algebra ブラックホール

项目摘要

In 1997 Eguchi, together with Hori and Xiong studied the topological string theory on a target space M and obtained an infinite sequence of differential operators which form a Viarsoro algebra with a central charge c = X(M) (X(M) denotes the Euler number of M). In 1998 Eguchi, together with Jinzenji and Xiong studied the free field realization of Virasoro operators and have shown that there exist a bosonic (fermionic) free field in 1+1 dimension for each even (odd) cohomology class of M. Eguchi together with Xiong further derived topological recursion relations valid in any genus using the result of 2-dimensional gravity and verified that the Viraosoro operators predict the correct nunber of holomorphic curves also in genus 2, 3. These results are now called Virasoro conjecture of quantum cohomology.It is well-known in string theory that the geometry of Calabi-Yau manifold may be described by Landau-Ginzburg theory (CY/LG correspondence). In the gauged linear (σ model it is possible to interpole between the regime of the classical geometry of a target manifold and the regime of local geometry of extrema of some superpotential by varying its parameter. 1999 Eguchi together with Jinzenji studied CY/LG correspondence and have shown that the correspondence holds even when M is not a Calabi-Yau manifold as far as it is a spin manifold.When the Calabi-Yau manifold degenerates and some of its cycle vanishes, there occur non-perturbative phenomena in string theory like gauge symmetry enhancement. Thus the analysis of string theory in singular Calabi-Yau manifold is of particular interest. Eguchi together with Sugawara studied the string propagation on singular Calabi-Yau manifolds and explicitly constructed modular invariant partition functions. Modular invariants are classified according the A-D-E pattern of isolated sigularities.

1997年，Eguchi与Hori和Xiong一起研究了目标空间M上的拓扑字符串理论，并获得了差分算子的无限序列，该序列形成具有中央电荷C = x（m）的Viarsoro代数（x（m）表示m）。 1998年，Eguchi与Jinzenji和Xiong一起研究了Virasoro操作员的自由田间实现，并表明，每个均匀（奇数）共同体的Eguchi M. Eguchi在1+1维度中存在掌声（费米子）的自由领域，并在eguchi中与eguchi M. Eguchi一起使用Xiong同变的拓扑效率和任何基因式的经验，并具有2 dimens的作用。在第2、3属中也预测了圆形曲线的正确肿瘤。这些结果现在称为Virasoro的量子同胞的猜想。它在字符串理论中众所周知，Calabi-yau歧管的几何形状可以由Landau-Ginzburg理论（CY/LG通讯）描述。在量规线性（σ模型中，可以通过改变其参数的参数来通过某种超级目标的局部几何形状与极端的局部几何形状进行插孔。1999eguchi eguchi与jinzenji cy/lg的cy/lg相应，并表明了与均不相差的情况。卡拉比（Calabi-Yau）流形的循环且有些循环消失，弦理论中存在非扰动现象，例如仪表对称性的增强不变性根据孤立的sigularition的A-D-E模式进行分类。