arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2210.14865hep-th
收藏

开超弦有效作用量中单圈矩阵元的颜色-运动学对偶表示

Color-kinematics dual representations of one-loop matrix elements in the open-superstring effective action

Alex Edison, Micah Tegevi

备注：
29 pages, 1 figure, 3 tables; v2: Updated discussion of zeta_7, including new representation
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

AI总结：

本文研究了开超弦中单圈四点高维算子插入的颜色-运动学对偶表示，成功构造了 $ζ_3$、$ζ_5$ 和 $ζ_3^2$ 的对偶分子，揭示了 $ζ_7$ 在外腿气泡图上的构造障碍，并探讨了双复制方法生成闭弦插入分子。

摘要：

弦理论的 $α'$ 展开提供了一组丰富的高维算子，以 $ζ$ 值为索引，可用于研究颜色-运动学对偶和双复制。这两个强大的性质实际上最早是在树图级弦振幅中被注意到的，它们简化了规范振幅和引力振幅的构造。然而，它们的适用性和局限性尚未被完全理解。我们尝试在单圈和四点处，为对应于开超弦中最低四个无 $ζ_2$ 算子插入（即 $ζ_3$、$ζ_5$、$ζ_3^2$ 和 $ζ_7$）的算子组合插入，构造一组颜色-运动学对偶分子。我们成功地为前三个找到了用盒形、三角形和气泡分子表示的表示形式。在 $ζ_7$ 的情况下，我们发现了一个阻碍完全颜色对偶表示的障碍，这与外腿气泡型图有关。我们讨论了解决这一障碍的两种途径，这两种途径都表明颜色-运动学对偶与展现某些期望性质之间存在不兼容性。使用所构造的颜色对偶分子，我们找到了两种不同的 Bern-Carrasco-Johansson 双复制，它们能产生候选的闭弦插入分子。这两种双复制方法都匹配了割线的运动学，其相对归一化由对包含简并在内的两种双复制求和，或在双复制分子定义上包含显式前置因子来设定。

英文摘要：

The $α'$-expansion of string theory provides a rich set of higher-dimension operators, indexed by $ζ$ values, which can be used to study color-kinematics duality and the double copy. These two powerful properties, actually first noticed in tree-level string amplitudes, simplify the construction of both gauge and gravity amplitudes. However, their applicability and limitations are not fully understood. We attempt to construct a set of color-kinematics dual numerators at one loop and four points for insertions of operator combinations corresponding to the lowest four $ζ_2$-free operator insertions from the open superstring: $ζ_3$, $ζ_5$, $ζ_3^2$, and $ζ_7$. We succeed in finding a representation for the first three in terms of box, triangle, and bubble numerators. In the case of $ζ_7$ we find an obstruction to a fully color-dual representation related to the bubble-on-external-leg type diagrams. We discuss two paths around this obstruction, both of which signal an incompatability between color-kinematics duality and manifesting certain desired properties. Using the constructed color-dual numerators, we find two different Bern-Carrasco-Johansson double copies that produce candidate closed-string-insertion numerators. Both approaches to the double copy match the kinematics of the cuts, with relative normalization set by either summing over both double copies including degeneracy or by including an explicit prefactor on the double-copy numerator definitions.

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。

↑