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arXiv 0710.3480hep-thgr-qc
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彭罗斯极限与字符串扩展

Penrose Limits vs String Expansions

Matthias Blau, Sebastian Weiss

摘要:

本文分析了一般弯曲背景下弦运动方程和约束的两种先验完全不同的展开式之间的关系,即一种是基于零测地线γ的彭罗斯极限平面波周围度规G_{μν}的协变彭罗斯-费米展开式,另一种是基于零测地线γ周围弦嵌入变量的精确度规G_{μν}中的黎曼坐标展开式。从观察到平面波中的精确弦方程与一般背景下的一阶弦方程之间存在形式上的相似性开始,我们证明了只要背景弦组态是零测地线γ本身,这种相似性就变得精确。然后,我们探索这两个扩展之间的高阶对应关系,并发现,对于一般弯曲的背景,他们同意所有的订单,只要一个工作在费米坐标和光锥规范。此外,要求共形规范限制一个通常类的(布林克曼)背景同时承认光锥和共形规范,没有进一步的限制。

英文摘要:

We analyse the relation between two a priori quite different expansions of the string equations of motion and constraints in a general curved background, namely one based on the covariant Penrose-Fermi expansion of the metric G_{μν} around a Penrose limit plane wave associated to a null geodesic γ, and the other on the Riemann coordinate expansion in the exact metric G_{μν} of the string embedding variables around the null geodesic γ. Starting with the observation that there is a formal analogy between the exact string equations in a plane wave and the first order string equations in a general background, we show that this analogy becomes exact provided that one chooses the background string configuration to be the null geodesic γitself. We then explore the higher-order correspondence between these two expansions and find that for a general curved background they agree to all orders provided that one works in Fermi coordinates and in the lightcone gauge. Requiring moreover the conformal gauge restricts one to the usual class of (Brinkmann) backgrounds admitting simultaneously the lightcone and the conformal gauge, without further restrictions.

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