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arXiv 0710.4907hep-th
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U-对偶与紧化Gauss-Bonnet项

U-Duality and the Compactified Gauss-Bonnet Term

Ling Bao, Johan Bielecki, Martin Cederwall, Bengt E. W. Nilsson, Daniel Persson

摘要:

本文给出了Gauss-Bonnet拉格朗日量从D维到(D-n)维的完全环面紧化。我们的目标是调查由此产生的行动的角度来看,“U-对偶”对称SL(n+1,R),这是目前在树级拉格朗日当D-n=3。该分析建立在论文[arXiv:0706.1183]的基础上并扩展了该论文的研究,通过详细计算紧化高斯-博内项的完整结构,包括来自于高斯-博内项指数的贡献。我们分析这些指数使用的表示理论的李代数sl(n+1,R),并确定表示似乎是相关的二次曲率校正。通过解释作为一个大的体积膨胀的SL(n+1,Z)不变的行动的主导项的紧化的结果,我们得出结论,整体指数的非线性因子不应该包括在表示结构。因此,所有的非对称指数都对应于sl(n+1,R)的权重,尽管如此,sl(n+1,R)仍然保持在根格的正侧。

英文摘要:

We present the complete toroidal compactification of the Gauss-Bonnet Lagrangian from D dimensions to (D-n) dimensions. Our goal is to investigate the resulting action from the point of view of the "U-duality" symmetry SL(n+1,R) which is present in the tree-level Lagrangian when D-n=3. The analysis builds upon and extends the investigation of the paper [arXiv:0706.1183], by computing in detail the full structure of the compactified Gauss-Bonnet term, including the contribution from the dilaton exponents. We analyze these exponents using the representation theory of the Lie algebra sl(n+1,R) and determine which representation seems to be the relevant one for quadratic curvature corrections. By interpreting the result of the compactification as a leading term in a large volume expansion of an SL(n+1,Z)-invariant action, we conclude that the overall exponential dilaton factor should not be included in the representation structure. As a consequence, all dilaton exponents correspond to weights of sl(n+1,R), which, nevertheless, remain on the positive side of the root lattice.

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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