论文标题
世界表的裁员
Unitarity Cuts of the Worldsheet
论文作者
论文摘要
我们计算一个属的弦散射幅度的虚部。在Witten的$ i \ varepsilon $处方中，用于在世界表格的模量空间上的集成轮廓，我们给出了一种一般算法，用于计算Annulus，Möbius条和Torus Topologies的计算单位性削减量。在热带分析的帮助下，我们展示了阈值的复杂模式（正常和异常）是如何源于世界表格计算的。结果是振幅虚构部分的明显结合表示，该幅度具有现场理论中的Cutkosky规则所期望的分析形式，但绕开了对中级状态进行费力的总和的需求。我们使用这种表示来研究字符串振幅的各个物理方面，包括它们在$（s，t）$平面中的行为，指数抑制，巨大的字符串的衰减宽度，总横截面和低能膨胀。我们发现平面环振幅幅度具有低型旋转优势的版本：在任何有限的能量下，只有有限数量的低部分波浪旋转为假想部分做出了可观的贡献。
We compute the imaginary parts of genus-one string scattering amplitudes. Following Witten's $i\varepsilon$ prescription for the integration contour on the moduli space of worldsheets, we give a general algorithm for computing unitarity cuts of the annulus, Möbius strip, and torus topologies exactly in $α'$. With the help of tropical analysis, we show how the intricate pattern of thresholds (normal and anomalous) opening up arises from the worldsheet computation. The result is a manifestly-convergent representation of the imaginary parts of amplitudes, which has the analytic form expected from Cutkosky rules in field theory, but bypasses the need for performing laborious sums over the intermediate states. We use this representation to study various physical aspects of string amplitudes, including their behavior in the $(s,t)$ plane, exponential suppression, decay widths of massive strings, total cross section, and low-energy expansions. We find that planar annulus amplitudes exhibit a version of low-spin dominance: at any finite energy, only a finite number of low partial-wave spins give an appreciable contribution to the imaginary part.
