论文标题
到尖端和背部：模块化图功能的复兴分析
To the cusp and back: Resurgent analysis for modular graph functions
论文作者
论文摘要
模块化图功能在计算封闭串散射幅度的低能扩张的计算中出现。对于环形世界表，它们是$ {\ rm sl}（2，\ mathbb {z}）$ - 圆环复杂结构的不变函数，必须集成在不等性tori的Moduli空间上。当模块化图函数的参数接近此模量空间时，我们使用复苏分析中的方法来构建非扰动校正。 $ {\ rm sl}（2，\ mathbb {z}）$ - 不变依次会强烈约束非扰动扇区的行为，而在Moduli空间的原点上展开。
Modular graph functions arise in the calculation of the low-energy expansion of closed-string scattering amplitudes. For toroidal world-sheets, they are ${\rm SL}(2,\mathbb{Z})$-invariant functions of the torus complex structure that have to be integrated over the moduli space of inequivalent tori. We use methods from resurgent analysis to construct the non-perturbative corrections arising when the argument of the modular graph function approaches the cusp on this moduli space. ${\rm SL}(2,\mathbb{Z})$-invariance will in turn strongly constrain the behaviour of the non-perturbative sector when expanded at the origin of the moduli space.
