arXiv 0905.21872009-05hep-th

从Chern-Simons引力论看标准广义相对论

Standard General Relativity from Chern-Simons Gravity

Fernando Izaurieta, Paul Minning, Alfredo Pérez, Eduardo Rodríguez, Patricio Salgado

备注：: 6 pages, no figures; v2: published version
发表信息：: Phys.Lett.B678:213-217,2009
DOI：: 10.1016/j.physletb.2009.06.017

摘要：

Chern-Simons引力模型是有趣的，因为它们在纤维束意义上提供了一个真正的规范不变作用原理。到目前为止，它们的主要缺点主要是与标准的广义相对论相距甚远，因为拉格朗日量中存在更高的曲率幂（除了三维时空）。在这里，我们报告一个简单的模型，提出了一种机制，通过这种机制，五维时空中的标准广义相对论可能确实出现在耦合空间中的一个特殊临界点，在那里，额外的自由度和相应的“反常”高斯-邦纳约束从陈-西蒙斯作用量中消失。为了达到这个结果，李代数g和对称g-不变张量，定义的Chern-Simons拉格朗日通过李代数S-展开方法与适当的有限交换半群S构造。结果被推广到任意奇数维，并简要讨论了可能的扩展到十一维超引力的情况。

英文摘要：

Chern-Simons models for gravity are interesting because they provide with a truly gauge-invariant action principle in the fiber-bundle sense. So far, their main drawback has largely been the perceived remoteness from standard General Relativity, based on the presence of higher powers of the curvature in the Lagrangian (except, remarkably, for three-dimensional spacetime). Here we report on a simple model that suggests a mechanism by which standard General Relativity in five-dimensional spacetime may indeed emerge at a special critical point in the space of couplings, where additional degrees of freedom and corresponding "anomalous" Gauss-Bonnet constraints drop out from the Chern-Simons action. To achieve this result, both the Lie algebra g and the symmetric g-invariant tensor that define the Chern-Simons Lagrangian are constructed by means of the Lie algebra S-expansion method with a suitable finite abelian semigroup S. The results are generalized to arbitrary odd dimensions, and the possible extension to the case of eleven-dimensional supergravity is briefly discussed.

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