Title: Superstring amplitudes from the field-theory limit: an n-point map at one loop Show Chinese title

Title: 从场论极限中的超弦振幅：一环n点映射

Abstract: Are perturbative superstring amplitudes for massless external states just an $\alpha'$ dressing of super-Yang-Mills/supergravity? This is the case at tree level, where the worldsheet correlators at $n$ points can be written in a natural worldsheet basis, such that the kinematic coefficients are BCJ numerators of super-Yang-Mills/supergravity amplitudes, with the non-trivial $\alpha'$ dependence carried only by the Koba-Nielsen factor. Motivated by this construction, we present for the first time a complete worldsheet basis of one-loop superstring correlators at $n$ points. All the kinematic coefficients associated to non-cusp basis elements are identified with pieces of one-loop BCJ numerators of super-Yang-Mills/supergravity. This determines the superstring correlators up to 15 points in terms of field theory. Starting at 16 points (modular weight 12), the worldsheet basis may include cusp forms, which vanish in the field-theory degeneration, such that the associated coefficients cannot be fixed in this manner. Therefore, the one-loop answer to our initial question is determined, at high multiplicity, by whether the coefficients of cusp basis elements vanish or not. As a by-product of our construction, we present new constraints on the field-theory limit that result from string modularity. These are expressed as additional relations among one-loop BCJ numerators in maximal super-Yang-Mills/supergravity starting at 6 points. Show Chinese abstract

Abstract: 微扰超弦振幅对于无质量外部态是否仅仅是超杨-米尔斯/超引力的$\alpha'$修饰？ 在树图级别上是这种情况，其中在$n$个点的世界面关联函数可以以自然的世界面基的形式写出，使得动量系数是超杨-米尔斯/超引力振幅的BCJ数值，非平凡的$\alpha'$依赖性仅由Koba-Nielsen因子携带。 受此构造的启发，我们首次提出了一个完整的单圈超弦关联函数在$n$个点的世界面基。 所有与非尖点基元素相关的动量系数都被识别为单圈BCJ数值的超杨-米尔斯/超引力部分。 这使得超弦关联函数在15个点以内可以通过场论来确定。 从16个点（模权12）开始，世界面基可能包含在场论退化中消失的尖点形式，因此这些相关系数不能以这种方式确定。 因此，在高多重性下，我们最初问题的单圈答案取决于尖点基元素系数是否为零。 作为我们构造的副产品，我们提出了来自字符串模性的场论极限的新约束。 这些约束表现为从6个点开始的极大超杨-米尔斯/超引力单圈BCJ数值之间的额外关系。