论文标题
封闭和开放字符串的一环振幅（一环KLT关系）之间的关系
A Relation between One-Loop Amplitudes of Closed and Open Strings (One-Loop KLT Relation)
论文作者
论文摘要
我们表达一环封闭的字符串振幅，为打开字符串单环子放大正方形的加权总和。这些发现概括了 - 受最终复杂结构模量整合的限制 - 著名的树级关系称为kawai -lewellen -tye（KLT）与较高回路的关系，并可以用于无质量和大规模的案例 - 有或没有超对称性。结果，在现场理论中，我们的关系资本化了固体的单循环量规关系关系，包括循环级别的颜色运动学双重性。特别是，在引力一环振幅中，重力被交换了两个胶状，就像在树级时一样。我们的结果是通过将每个复杂的弦线坐标划分为两个真实圆柱坐标的基础字符串世界表圆环的，该曲线通过椭圆曲线上的分析延续分解为一对两个真实的圆柱坐标。这种操作涉及循环动量，该动量介导了两个一环弦缸振幅之间。
We express one-loop closed string amplitudes as weighted sums over squares of open string one-loop subamplitudes. These findings generalize - subject to final complex structure modulus integration - the celebrated tree-level relationships known as Kawai-Lewellen-Tye (KLT) relations to higher loops and can be applied for both the massless and massive case - with or without supersymmetry. As a consequence in the field-theory limit our relations capitalize solid one-loop gauge-gravity relations including loop-level color kinematics duality. In particular, in gravitational one-loop amplitudes a graviton is traded for two gluons just like at tree-level. Our results are derived on the underlying string world-sheet torus by splitting each complex string coordinate into a pair of two real cylinder coordinates by means of an analytic continuation on the elliptic curve. This manipulation involves the loop momentum, which mediates between the two one-loop open string cylinder amplitudes.
