广义Vielbeins和非线性实现
Generalised vielbeins and non-linear realisations
摘要：
我们简要地回顾为什么非线性实现的半直接产品的一组其表示之一，导致一个场论上定义的广义时空配备了广义维尔本。我们给出公式，其中只涉及矩阵乘法，为广义vielbein，嘉当形式及其变换。我们考虑在2003年引入的广义时空的背景下，E（11）和它的第一基本表示的半直积的非线性实现。对于后者的理论，我们给出了明确的表达式，广义vielbein，并包括与双引力子在四，五，十一维和IIB理论在十维的水平。我们还计算了广义vielbein，直到类似的水平，为非常扩展的SL（2）与其第一基本表示的半直积的非线性实现，这是一个与四维引力相关的理论。
英文摘要：
We briefly review why the non-linear realisation of the semi-direct product of a group with one of its representations leads to a field theory defined on a generalised space-time equipped with a generalised vielbein. We give formulae, which only involve matrix multiplication, for the generalised vielbein, the Cartan forms and their transformations. We consider the generalised space-time introduced in 2003 in the context of the non-linear realisation of the semi-direct product of E(11) and its first fundamental representation. For this latter theory we give explicit expressions for the generalised vielbein up to and including the levels associated with the dual graviton in four, five and eleven dimensions and for the IIB theory in ten dimensions. We also compute the generalised vielbein, up to the analogous level, for the non-linear realisation of the semi-direct product of very extended SL(2) with its first fundamental representation, which is a theory associated with gravity in four dimensions.
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