论文标题
稳定曲线的散射幅度
Scattering amplitudes of stable curves
论文作者
论文摘要
由Castravet和Tevelev引入的Grethendieck-Knudsen Moduli在Gretendieck-Knudsen Moduli空间上的平均分隔线的方程式出现在N = 4 Yang-Mills理论中N = 4 Yang-Mills理论的散射幅度形式的分子中，在Arkani Hamed，Bourjaily，Bourjaily，bourjaily，cachazo，Postnikov和tronka中。这只是代数几何和高能量物理学之间令人兴奋的关系的冰山一角，而不是巧合。 We interpret leading singularities of scattering amplitude forms of massless particles as probabilistic Brill-Noether theory: the study of statistics of images of n marked points under a random meromorphic function uniformly distributed with respect to the translation-invariant volume form of the Jacobian.我们专注于违反制度的最大螺旋性，这为各种代数曲线提供了美丽的物理启发的几何形状：光滑，稳定，稳定，过度，真实的代数等。
Equations of hypertree divisors on the Grothendieck-Knudsen moduli space of stable rational curves, introduced by Castravet and Tevelev, appear as numerators of scattering amplitude forms for n massless particles in N=4 Yang-Mills theory in the work of Arkani-Hamed, Bourjaily, Cachazo, Postnikov and Trnka. Rather than being a coincidence, this is just the tip of the iceberg of an exciting relation between algebraic geometry and high energy physics. We interpret leading singularities of scattering amplitude forms of massless particles as probabilistic Brill-Noether theory: the study of statistics of images of n marked points under a random meromorphic function uniformly distributed with respect to the translation-invariant volume form of the Jacobian. We focus on the maximum helicity violating regime, which leads to a beautiful physics-inspired geometry for various classes of algebraic curves: smooth, stable, hyperelliptic, real algebraic, etc.
