arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 0909.1718hep-thmath.DG
收藏

D=6中新的非紧Calabi-Yau度量

New non compact Calabi-Yau metrics in D=6

Osvaldo P. Santillan

备注：
A numerical error has been corrected together with the corresponding analysis of the metric
发表信息：
Class.Quant.Grav.27:155013,2010
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

本文给出了一种利用初始超卡勒结构构造六维显式Calabi-Yau度量的方法。要求解的方程通常是非线性的，但当描述度量的对象仅依赖于超卡勒四维空间的一个复坐标及其复共轭时，方程就变成线性的。这种情况特别给出了在超卡勒空间内包裹复1-圈的D 6-膜的对偶描述，这是由Fayyazuddin研究的。本文工作推广了他给出的结构。但我们给出的显式解对应于非线性问题。这是一个关于两个变量的非线性方程，借助于某些特定的anzatz，它被简化为一个单变量的非线性方程，可以用椭圆函数来求解。在这些条件下，我们构造了一个非紧的Calabi-Yau度量的无限族。

英文摘要：

A method for constructing explicit Calabi-Yau metrics in six dimensions in terms of an initial hyperkahler structure is presented. The equations to solve are non linear in general, but become linear when the objects describing the metric depend on only one complex coordinate of the hyperkahler 4-dimensional space and its complex conjugated. This situation in particular gives a dual description of D6-branes wrapping a complex 1-cycle inside the hyperkahler space, which was studied by Fayyazuddin. The present work generalize the construction given by him. But the explicit solutions we present correspond to the non linear problem. This is a non linear equation with respect to two variables which, with the help of some specific anzatz, is reduced to a non linear equation with a single variable solvable in terms of elliptic functions. In these terms we construct an infinite family of non compact Calabi-Yau metrics.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑