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arXiv 0912.3199hep-th
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五维极小超引力与带电旋转黑洞的可积性

Integrability of Five Dimensional Minimal Supergravity and Charged Rotating Black Holes

Pau Figueras, Ella Jamsin, Jorge V. Rocha, Amitabh Virmani

摘要:

我们探讨了五维极小超引力在三个交换Killing向量存在下的可积性。我们认为,看到的可积性结构的理论之一,必须执行一个埃勒斯减少到两个维度。直接降维到二维并不能使我们以一种容易的方式看到理论的可积性。这种情况与真空五维引力相反。基于陪集G2/(SL(2,R)× SL(2,R))的对称7 × 7陪集表示矩阵,导出了最小超引力下的Belinski-Zakharov(BZ)拉克斯对.我们阐明我们的BZ拉克斯对和群论拉克斯对以前已知的文献之间的关系。BZ拉克斯对使我们能够将著名的BZ修整方法推广到五维最小超引力。我们证明了三维隐对称变换对BZ dressing方法的作用仅仅是对BZ向量的群作用。作为我们的形式主义的一个例子,我们得到了双自旋五维Myers-Perry黑洞通过应用孤子变换的Schwarzschild黑洞。通过对Reissner-Nordstrom黑洞进行孤子变换,我们得到了Cvetic-Youm黑洞.

英文摘要:

We explore the integrability of five-dimensional minimal supergravity in the presence of three commuting Killing vectors. We argue that to see the integrability structure of the theory one necessarily has to perform an Ehlers reduction to two dimensions. A direct dimensional reduction to two dimensions does not allow us to see the integrability of the theory in an easy way. This situation is in contrast with vacuum five-dimensional gravity. We derive the Belinski-Zakharov (BZ) Lax pair for minimal supergravity based on a symmetric 7x7 coset representative matrix for the coset G2/(SL(2,R) x SL(2,R)). We elucidate the relationship between our BZ Lax pair and the group theoretic Lax pair previously known in the literature. The BZ Lax pair allows us to generalize the well-known BZ dressing method to five-dimensional minimal supergravity. We show that the action of the three-dimensional hidden symmetry transformations on the BZ dressing method is simply the group action on the BZ vectors. As an illustration of our formalism, we obtain the doubly spinning five-dimensional Myers-Perry black hole by applying solitonic transformations on the Schwarzschild black hole. We also derive the Cvetic-Youm black hole by applying solitonic transformations on the Reissner-Nordstrom black hole.

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