Kähler metrics and gauge kinetic functions for intersecting D6‐branes on toroidal orbifolds – The complete perturbative story
Kähler metrics and gauge kinetic functions for intersecting D6‐branes on toroidal orbifolds – The complete perturbative story
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环形轨道上相交的 D6 膜的凯勒度量和规范动力学函数 – 完整的微扰故事
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发表时间：
2011
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通讯作者：
G. Honecker
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作者：
G. Honecker
我们系统地推导了微扰精确的全纯规范动力学函数，开弦Kähler度量和闭弦Kähler势相交D 6-膜匹配开弦单圈计算的规范阈值与场论规范耦合？= 1超重力。我们考虑了T6/Ω上的体D 6-膜、分式D 6-膜和刚性D 6-膜的所有情形，以及没有和有离散挠率的轨道折叠T6/（N × Ω）和T6/（2 × 2 M × Ω），它们在体复结构的数量和体Kähler势上不同。我们的分析包括了D 6-膜和O 6-平面之间的所有消失角和非消失角的超对称构型，并考虑了所有可能的Wilson线和位移模量。凯勒模的形状与轨道无关，但与角度相关，而全纯规范动力学函数则得到三种不同的单圈修正：一种依赖于凯勒模，与轨道背景无关，与某个消失角相关;另一种依赖于复结构模，只与分数和刚性D 6膜相关;最后一种依赖于与O 6平面相交的常数项。这些结果对于构造唯象吸引力D膜模型的相关有效场论是至关重要的。作为第一个例子，我们计算了[1]中具有刚性D-膜的一些T6/102 × 102例子的完全微扰规范动力学函数和Kähler度量。作为第二类例子，给出了[2]中关于T6/T6 ′T6/T6 ′上标准模型的分数QCD和轻子D 6膜堆的Kähler度规和规范动力学函数。
We systematically derive the perturbatively exact holomorphic gauge kinetic function, the open string Kähler metrics and closed string Kähler potential on intersecting D6‐branes by matching open string one‐loop computations of gauge thresholds with field theoretical gauge couplings in ? = 1 supergravity. We consider all cases of bulk, fractional and rigid D6‐branes on T6/Ω ℛ and the orbifolds T6/(ℤN × Ω ℛ) and T6/(ℤ2 × ℤ2M × Ω ℛ) without and with discrete torsion, which differ in the number of bulk complex structures and in the bulk Kähler potential. Our analysis includes all supersymmetric configurations of vanishing and non‐vanishing angles among D6‐branes and O6‐planes, and all possible Wilson line and displacement moduli are taken into account. The shape of the Kähler moduli turns out to be orbifold independent but angle dependent, whereas the holomorphic gauge kinetic functions obtain three different kinds of one‐loop corrections: a Kähler moduli dependent one for some vanishing angle independently of the orbifold background, another one depending on complex structure moduli only for fractional and rigid D6‐branes, and finally a constant term from intersections with O6‐planes. These results are of essential importance for the construction of the related effective field theory of phenomenologically appealing D‐brane models. As first examples, we compute the complete perturbative gauge kinetic functions and Kähler metrics for some T6/ℤ2 × ℤ2 examples with rigid D‐branes of [1]. As a second class of examples, the Kähler metrics and gauge kinetic functions for the fractional QCD and leptonic D6‐brane stacks of the Standard Model on T6/ℤ6′T6/ℤ6′ from [2] are given.