标题： 树级闭弦振幅与混合弦振幅之间的关系 显示英文标题

标题： Relations between closed string amplitudes and mixed string amplitudes at tree-level

摘要： 本文研究了弦理论中树图层次下闭弦振幅与混合弦振幅之间的关系。 通过复变量的解析延拓，我们将闭弦振幅分解为涉及（$n-2$）开弦和一个闭弦的振幅。 提供了四点、五点和六点振幅的表达式，并给出了$n$弦的系统性表述。 本文讨论了在Wick旋转过程中沿无限管积分时可能出现的修正项。 在场论极限下，由于这些修正项属于次主导阶，因此可以忽略不计。 显示英文摘要

摘要： This paper investigates the relationships between closed and mixed string amplitudes at the tree level in string theory. Through the analytic continuation of complex variables, we establish a factorization of closed string amplitudes into those involving ($n-2$) open strings and a single closed string. Expressions for four-, five-, and six-point amplitudes are provided, along with systematic formulations for $n$ strings. The paper addresses possible correction terms arising from integration along infinite tubes during the Wick rotation process. In the field theory limit, the correction terms become negligible due to being of subleading order.