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arXiv 0704.2769hep-th
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八维空间中与背景无关的量子引力

Towards a Background Independent Quantum Gravity in Eight Dimensions

J. A. Nieto

摘要:

我们开始了一个八维背景独立的量子引力程序。我们首先考虑$D=d+1$维中的正则引力\textit{a la}“卡鲁扎-克莱因”。我们表明,我们的正则引力方法可以适用于四维自对偶引力的情况。此外,通过使用我们先前提出的八维Ashtekar自对偶引力形式主义的经典作用量,我们继续发展八维的正则方法。我们的构造考虑了不同的SO(8)对称破缺。特别是,破缺$SO(8)=S_{R}^{7}% \times S_{L}^{7}\times G_{2}$在我们的讨论中起着重要的作用。

英文摘要:

We start a program of background independent quantum gravity in eight dimensions. We begin by considering canonical gravity \textit{a la} "Kaluza-Klein" in $D=d+1$ dimensions. We show that our canonical gravity approach can be applied to the case of self-dual gravity in four dimensions. Further, by using our previously proposed classical action of Ashtekar self-dual gravity formalism in eight dimensions, we proceed to develop the canonical approach in eight dimensions. Our construction considers different SO(8) symmetry breakings. In particular, the breaking $SO(8)=S_{R}^{7}% \times S_{L}^{7}\times G_{2}$ plays an important role in our discussion.

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