论文标题
d3-brane超级实力解决方案来自ricci-flat指标的Kähler-Einstein表面的规范束
D3-brane supergravity solutions from Ricci-flat metrics on canonical bundles of Kähler-Einstein surfaces
论文作者
论文摘要
可以通过涉及谐波扭曲因子的经典Ansatz获得D3-Brane超级实力的D3-桥解决方案，而D3 Brane World-Sheet的平坦Minkowskian指标，第二个是ricci flat flat flat flat flatric，在适当的6二维横向空间上，两者都扭曲了WARP因子。特别值得关注的是，thecanical束的总空间在复杂的Kähler上2倍。在许多情况下，这种情况在考虑有限商的唱片的同时出现。当组为$ \ mathbb {z} _4 $时，复杂的2倍是带有su（2）Xu（1）等轴测的Kähler指标的第二个Hirzebruch表面。实际上，通过单个函数参数化了整个类别的类别，并且最好在Amsy Symblectic形式主义中进行描述。我们恢复了Kähler-Einstein指标的两个参数子类的存在，这些歧管是均为$ s^2 \ times s^2 $的流形，并详细研究了此类。这些流形的K“ ahler-Einstein性质允许通过Calabi Ansatz在其规范捆绑上构建RICCI平面度量，我们将其在amsy形式主义中重新铸造，得出了一些新的优雅公式。此外，我们还显示了与量相似的量子相似的，这是基准的，这是相似的，这是基准的，这是相似的。
D3-brane solutions of type IIB supergravity can be obtained by means a classical ansatz involving a harmonic warp factor and two summands, the first being the flat Minkowskian metric of the D3 brane world-sheet and the second a Ricci flat metric on a suitable 6-dimensional transverse space, both twisted by the warp factor. Of particular interest is the case of the total space of thecanonical bundle over a complex Kähler 2-fold. This situation emerges in many cases while considering the resolution of finite quotient singulaties. When the group is $\mathbb{Z}_4$, the complex 2-fold is the second Hirzebruch surface endowed with a Kähler metric having SU(2)xU(1) isometry. There is actually an entire class of such metrics parameterized by a single function, and best described in the AMSY symplectic formalism. We recover the existence of a two parameter subclass of Kähler-Einstein metrics on manifolds that are homeorphic to $S^2\times S^2$, and study in detail this class. The K"ahler-Einstein nature of these manifolds allows the construction of the Ricci flat metric on their canonical bundle via the Calabi Ansatz, which we recast in the AMSY formalism deriving some new elegant formulae. Furthermore we show the full integrability of the differential system of geodesics equations thanks to an additional conserved quantity that we unveil and which is similar to the Carter constant in the case of the Kerr metric.
