论文标题
在模量空间上整合两个弦属的两个弦
Integrating simple genus two string invariants over moduli space
论文作者
论文摘要
我们考虑一个sp（4，z）不变性表达，涉及川祖米 - Zhang（kz）不变的两个因素，每个因素是一个模块化图，一个带有一个链接的模块化图，在两个riemann表面的Moduli空间上有四个衍生物。对其进行操纵，我们表明，模块化图的线性组合的积分空间具有两个链接，而Kz不变性的平方则减小到边界积分。我们还考虑了SP（4，Z）不变性表达式，涉及Kz不变的三个因素和模量空间上的六个衍生物，从中，我们从模块化图的模量空间上的积分中不可或缺，并将三个链接减少到边界积分。在这两种情况下，边界项均完全由Kz不变性确定。我们表明两种积分都消失了。
We consider an Sp(4,Z) invariant expression involving two factors of the Kawazumi--Zhang (KZ) invariant each of which is a modular graph with one link, and four derivatives on the moduli space of genus two Riemann surfaces. Manipulating it, we show that the integral over moduli space of a linear combination of a modular graph with two links and the square of the KZ invariant reduces to a boundary integral. We also consider an Sp(4,Z) invariant expression involving three factors of the KZ invariant and six derivatives on moduli space, from which we deduce that the integral over moduli space of a modular graph with three links reduces to a boundary integral. In both cases, the boundary term is completely determined by the KZ invariant. We show that both the integrals vanish.
