标题： 从弦理论计算夸克质量 显示英文标题

标题： Computation of Quark Masses from String Theory

摘要： 我们基于神经网络技术，对异质弦理论在具有非标准嵌入的光滑卡拉比-丘三维流形上的物理杨-米尔斯耦合进行了数值计算。 该模型属于一类大型的异质线丛模型，这些模型之前已被确定，并且它们的低能谱与MSSM精确匹配，外加一些未带标准模型群电荷的场。 计算的相关量，即里奇平坦的卡拉比-丘度规、厄米特-杨-米尔斯丛度规以及调和丛值形式，都是通过训练合适的神经网络得到的。 为了举例说明，我们考虑了复结构模空间中的一个参数族。 在这个位置的每个点上的计算在单个十二核CPU上大约需要半天时间。 我们估计杨-米尔斯耦合的结果与预期的解析结果相差约10%。 我们发现物质场归一化的影响可能是显著的，并可能有助于生成分层耦合。 我们还演示了基于福比尼-施图迪度规及其对应于丛度规和丛值形式的零阶半解析计算，结果大致正确，但与数值结果相差约25%。 该方法可以应用于其他异质线丛模型，并推广到其他构造中，包括F理论模型。 显示英文摘要

摘要： We present a numerical computation, based on neural network techniques, of the physical Yukawa couplings in a heterotic string theory compactification on a smooth Calabi-Yau threefold with non-standard embedding. The model belongs to a large class of heterotic line bundle models that have previously been identified and whose low-energy spectrum precisely matches that of the MSSM plus fields uncharged under the Standard Model group. The relevant quantities for the calculation, that is, the Ricci-flat Calabi-Yau metric, the Hermitian Yang-Mills bundle metrics and the harmonic bundle-valued forms, are all computed by training suitable neural networks. For illustration, we consider a one-parameter family in complex structure moduli space. The computation at each point along this locus takes about half a day on a single twelve-core CPU. Our results for the Yukawa couplings are estimated to be within 10% of the expected analytic result. We find that the effect of the matter field normalisation can be significant and can contribute towards generating hierarchical couplings. We also demonstrate that a zeroth order, semi-analytic calculation, based on the Fubini-Study metric and its counterparts for the bundle metric and the bundle-valued forms, leads to roughly correct results, about 25% away from the numerical ones. The method can be applied to other heterotic line bundle models and generalised to other constructions, including to F-theory models.