论文标题
依赖模量的卡拉比Yau和su（3） - 机器学习的结构指标
Moduli-dependent Calabi-Yau and SU(3)-structure metrics from Machine Learning
论文作者
论文摘要
我们使用机器学习来近似Calabi-yau和SU（3）结构指标，包括首次复杂结构模量依赖性。我们的新方法在准确性和速度方面改善了现有的数值近似值。了解这些指标具有许多应用，包括弦乐耦合的有效现场理论的关键方面的计算，例如Yukawa耦合的规范归一化以及在Swampland猜想中起着至关重要的作用的巨大弦乐频谱，到镜像对称和Syz的猜测。在SU（3）结构的情况下，我们的机器学习方法使我们能够设计具有某些扭转属性的指标。我们的方法是针对Calabi-Yau和SU（3） - 基于$ \ Mathbb {p}^的单参数家族的结构歧管（3）。
We use machine learning to approximate Calabi-Yau and SU(3)-structure metrics, including for the first time complex structure moduli dependence. Our new methods furthermore improve existing numerical approximations in terms of accuracy and speed. Knowing these metrics has numerous applications, ranging from computations of crucial aspects of the effective field theory of string compactifications such as the canonical normalizations for Yukawa couplings, and the massive string spectrum which plays a crucial role in swampland conjectures, to mirror symmetry and the SYZ conjecture. In the case of SU(3) structure, our machine learning approach allows us to engineer metrics with certain torsion properties. Our methods are demonstrated for Calabi-Yau and SU(3)-structure manifolds based on a one-parameter family of quintic hypersurfaces in $\mathbb{P}^4.$
