环面上的CHY-图
CHY-Graphs on a Torus
摘要：
最近，我们提出了一种新的方法，使用穿孔椭圆曲线的CHY框架，以计算单圈散射振幅。在本文中，我们进一步发展了这种方法，通过引入一组连接符，这成为主要成分，以建立在$\mathfrak{M}_{1,n}$，模空间的n-穿孔椭圆曲线的被积。作为一个特殊的应用，我们研究了$Φ^3$双伴随标量理论。我们提出了一套规则，构造的被积在$\mathfrak{M}_{1,n}$上的$Φ^ 3$被积在$\mathfrak{M}_{0,n}$，模空间的n-穿孔球。我们通过计算各种$Φ^3$单圈费曼图来说明这些规则。相反，我们也提供了另一套规则来计算相应的CH-被积函数的$\mathfrak{M}_{1,n}$，而不是从一个给定的$Φ^ 3$单圈费曼图。此外，我们的结果可以很容易地扩展到更高的循环。
英文摘要：
Recently, we proposed a new approach using a punctured Elliptic curve in the CHY framework in order to compute one-loop scattering amplitudes. In this note, we further develop this approach by introducing a set of connectors, which become the main ingredient to build integrands on $\mathfrak{M}_{1,n}$, the moduli space of n-punctured Elliptic curves. As a particular application, we study the $Φ^3$ bi-adjoint scalar theory. We propose a set of rules to construct integrands on $\mathfrak{M}_{1,n}$ from $Φ^ 3$ integrands on $\mathfrak{M}_{0,n}$, the moduli space of n-punctured spheres. We illustrate these rules by computing a variety of $Φ^3$ one-loop Feynman diagrams. Conversely, we also provide another set of rules to compute the corresponding CHY-integrand on $\mathfrak{M}_{1,n}$ by starting instead from a given $Φ^ 3$ one-loop Feynman diagram. In addition, our results can easily be extended to higher loops.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
