标题： Hadamard 乘积和 BPS 网络 显示英文标题

标题： Hadamard products and BPS networks

摘要： 我们研究四阶Picard-Fuchs算子的例子，这些算子是两个二阶Picard-Fuchs算子的Hadamard乘积。 每个二阶Picard-Fuchs算子与一族椭圆曲线相关联，而Hadamard乘积计算两个椭圆曲面的纤维积上的周期积分。 我们在这种几何结构上构造3-循环，作为基底上回路覆盖下的2-循环的并集。 然后我们使用特殊的拉格朗日条件来限制基底上的回路。 这导致了一种类似于在弦理论文献中之前出现的谱网络和指数网络的构造。 显示英文摘要

摘要： We study examples of fourth-order Picard-Fuchs operators that are Hadamard products of two second-order Picard-Fuchs operators. Each second-order Picard-Fuchs operator is associated with a family of elliptic curves, and the Hadamard product computes period integrals on the fibred product of the two elliptic surfaces. We construct 3-cycles on this geometry as the union of 2-cycles in the fibre over contours on the base. We then use the special Lagrangian condition to constrain the contours on the base. This leads to a construction that is reminiscent of spectral networks and exponential networks that have previously appeared in string theory literature.