arXiv 2402.016152024-02hep-th

从弦论计算夸克质量

Computation of Quark Masses from String Theory

Andrei Constantin, Kit Fraser-Taliente, Thomas R. Harvey, Andre Lukas, Burt Ovrut

备注：: Dedicated to the memory of Graham G. Ross

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AI总结：

本文利用神经网络数值求解杂化弦论 Calabi-Yau 紧致化中的几何与丛场量，从而计算物理 Yukawa 耦合，并验证其精度与可推广性。

摘要：

我们提出了一项基于神经网络技术的数值计算，用于计算在具有非标准嵌入的光滑 Calabi-Yau 三维流形上进行杂化弦论紧致化时的物理 Yukawa 耦合。该模型属于一大类此前已被识别出的杂化线丛模型，其低能谱与 MSSM 的能谱以及在 Standard Model 群下不带荷的场精确匹配。计算所涉及的相关量，即 Ricci 平坦 Calabi-Yau 度规、Hermitian Yang-Mills 丛度规以及调和的丛值形式，均通过训练合适的神经网络来计算。作为示例，我们考虑复结构模空间中的一个单参数族。沿此轨迹在每个点进行计算，在单个十二核 CPU 上大约需要半天时间。我们得到的 Yukawa 耦合结果估计在预期解析结果的 10% 以内。我们发现，物质场归一化的影响可能非常显著，并可有助于产生层级化耦合。我们还证明，基于 Fubini-Study 度规及其丛度规和丛值形式对应物的零阶半解析计算可给出大致正确的结果，与数值结果相差约 25%。该方法可应用于其他杂化线丛模型，并可推广到包括 F-理论模型在内的其他构造。

英文摘要：

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.

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