arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1601.07571hep-th
收藏

不同角度的分段字符串

Segmented strings from a different angle

David Vegh

摘要:

平坦空间中的分段弦是分段线性经典弦解。线段之间的扭结以光速移动,它们的世界线在世界面上形成一个晶格。这个想法可以推广到AdS $_3$,其中嵌入是从AdS $_2$补丁构建的。该构造提供了非线性弦运动方程的精确离散。本文利用扭结向量构造交比来计算分割字符串的面积。交比可以用左手变量或右手变量表示。AdS $_3$中的弦运动方程被简化为可积的时间离散的相对论Toda型晶格的弦运动方程。正解产生的串嵌入在全局变换下是唯一的。在附录中,Poincare目标空间能量通过沿扭结世界线积分世界片电流来计算,并推导出嵌入的积分标量曲率的公式。

英文摘要:

Segmented strings in flat space are piecewise linear classical string solutions. Kinks between the segments move with the speed of light and their worldlines form a lattice on the worldsheet. This idea can be generalized to AdS$_3$ where the embedding is built from AdS$_2$ patches. The construction provides an exact discretization of the non-linear string equations of motion. This paper computes the area of segmented strings using cross-ratios constructed from the kink vectors. The cross-ratios can be expressed in terms of either left-handed or right-handed variables. The string equation of motion in AdS$_3$ is reduced to that of an integrable time-discretized relativistic Toda-type lattice. Positive solutions yield string embeddings that are unique up to global transformations. In the appendix, the Poincare target space energy is computed by integrating the worldsheet current along kink worldlines and a formula is derived for the integrated scalar curvature of the embedding.

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。

↑