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arXiv 1206.2667hep-th
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S_5上IIB超引力紧化的球谐函数

Spherical harmonics for the compactification of IIB supergravity on S_5

Peter van Nieuwenhuizen

摘要:

本文详细推导了1985年Kim,Romans和作者关于IIB超引力在$S_5$上的Kaluza-Klein降维为5维最大反de Sitter超引力的论文中的谱所对应的球谐函数。我们展示了如何在文献中使用的所有方法,以获得光谱,如果内部空间是$S_n$可以来自嵌入$S_n$在$R^{n+1}$。对于自旋1/2球谐函数的一个重要观察是,如果变换到极坐标或球极坐标,也需要局部洛伦兹旋转。还导出了与电磁场矢量球谐函数的关系。

英文摘要:

We give a detailed derivation of the spherical harmonics which correspond to the spectrum in the tables of the 1985 paper by Kim, Romans and the author on the Kaluza-Klein dimensional reduction of IIB supergravity on $S_5$ to 5-dimensional maximal anti de Sitter supergravity. We show how all methods that have been used in the literature to obtain spectra if the internal space is $S_n$ can be derived from embedding $S_n$ in $R^{n+1}$. A crucial observation for spin 1/2 spherical harmonics is that one also needs a local Lorentz rotation if one transforms to polar or stereographic coordinates. The relation to the vector spherical harmonics of electromagnetism is also worked out.

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。

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