From ten to four and back again: how to generalize the geometry
From ten to four and back again: how to generalize the geometry
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从十到四再回来：如何概括几何
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发表时间：
2007
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通讯作者：
L. Martucci
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作者：
Paul Koerber;L. Martucci
讨论了在AdS 4或平坦Minkowski时空中研究SU（3）× SU（3）-结构的翘曲II型通量紧化的四维N = 1有效方法.非平凡的扭曲使得它自然地使用超重力公式不变下的局部复杂化外尔变换。我们从涉及域壁和广义校准的标准参数中获得经典超势，并展示了由此产生的F-平坦性和D-平坦性方程如何精确地再现完整的十维超对称方程。此外，我们考虑了非微扰修正的效果，这个超势产生的高根诺凝聚或欧几里德D-膜瞬子。对于后者，我们导出了N = 1通量真空中的超对称性条件。我们发现非微扰修正引起了内部广义几何的量子形变。涂抹瞬子允许从十维的角度来理解KKLT类AdS真空。另一方面，非涂抹瞬子IIB扭曲卡-丘紧化“不稳定”的卡-丘复杂的结构成为一个真正的广义复杂的。这种变形给出了由非微扰修正引起的移动的D3-膜的非平凡超势的几何解释。
We discuss the four-dimensional N = 1 effective approach in the study of warped type II flux compactifications with SU(3) × SU(3)-structure to AdS4 or flat Minkowski space-time. The non-trivial warping makes it natural to use a supergravity formulation invariant under local complexified Weyl transformations. We obtain the classical superpotential from a standard argument involving domain walls and generalized calibrations and show how the resulting F-flatness and D-flatness equations exactly reproduce the full ten-dimensional supersymmetry equations. Furthermore, we consider the effect of non-perturbative corrections to this superpotential arising from gaugino condensation or Euclidean D-brane instantons. For the latter we derive the supersymmetry conditions in N = 1 flux vacua in full generality. We find that the non-perturbative corrections induce a quantum deformation of the internal generalized geometry. Smeared instantons allow to understand KKLT-like AdS vacua from a ten-dimensional point of view. On the other hand, non-smeared instantons in IIB warped Calabi-Yau compactifications `destabilize' the Calabi-Yau complex structure into a genuine generalized complex one. This deformation gives a geometrical explanation of the non-trivial superpotential for mobile D3-branes induced by the non-perturbative corrections.