论文标题
杂丝弦理论中的全态育川耦合
Holomorphic Yukawa Couplings in Heterotic String Theory
论文作者
论文摘要
本论文与杂型E8 X E8弦模型有关，这些模型可以在低能极限下产生标准模型的甲酸n = 1个超对称扩展。我们通常是通过从十维理论中得出四维谱和拉格朗日术语开始的，这是通过对六维的calabi-yau歧管的压实过程开始的，将全体形态多态矢量束定义在其上。然后，我们专门研究一类杂弦模型，该模型将向量束分为线束的总和，而Calabi-yau歧管被定义为投影型环境空间中的完整交集。我们开发了一种通过将卡拉比（Calabi-Yau）歧管上的捆绑值与其环境空间对应物相关联的束值形式来计算这些模型的全体形态Yukawa耦合的方法，以便可以在投射空间上评估相关的积分。该方法适用于文献中已知的7890个晶状体歧管中的任何一个，我们表明它可以与早期的代数技术有关，以计算Holomorphic Yukawa耦合。我们为在四季度压缩的模型和两个圆环的同性含量上提供明确计算。制定了消失的定理，表明在某些情况下，拓扑而不是对称是缺乏某些三联耦合的原因。另外，发现一些Yukawa矩阵取决于复杂的结构模量，并且在模量空间的某些区域中，其等级降低。在最后一部分中，我们专注于一种评估物质领域的方法，而不知道Ricci-flat calabi-yau指标。这对于大型内部量规通量是可能的，而紧凑型歧管上的点附近的正常化积分位置。
This thesis is concerned with heterotic E8 x E8 string models that can produce quasirealistic N = 1 supersymmetric extensions of the Standard Model in the low-energy limit. We start rather generally by deriving the four-dimensional spectrum and Lagrangian terms from the ten-dimensional theory, through a process of compactification over six-dimensional Calabi-Yau manifolds, upon which holomorphic poly-stable vector bundles are defined. We then specialise to a class of heterotic string models for which the vector bundle is split into a sum of line bundles and the Calabi-Yau manifold is defined as a complete intersection in projective ambient spaces. We develop a method for calculating holomorphic Yukawa couplings for such models, by relating bundle-valued forms on the Calabi-Yau manifold to their ambient space counterparts, so that the relevant integrals can be evaluated over projective spaces. The method is applicable for any of the 7890 CICY manifolds known in the literature, and we show that it can be related to earlier algebraic techniques to compute holomorphic Yukawa couplings. We provide explicit calculations of the holomorphic Yukawa couplings for models compactified on the tetra-quadric and on a co-dimension two CICY. A vanishing theorem is formulated, showing that in some cases, topology rather than symmetry is responsible for the absence of certain trilinear couplings. In addition, some Yukawa matrices are found to be dependent on the complex structure moduli and their rank is reduced in certain regions of the moduli space. In the final part, we focus on a method to evaluate the matter field Kahler potential without knowing the Ricci-flat Calabi-Yau metric. This is possible for large internal gauge fluxes, for which the normalisation integral localises around a point on the compactification manifold.
