In this article, we establish in a rigorous mathematical way that Koba-Nielsen amplitudes defined on any local field of characteristic zero are bona fide integrals that admit meromorphic continuations in the kinematic parameters. Our approach allows us to study in a uniform way open and closed Koba-Nielsen amplitudes over arbitrary local fields of characteristic zero. In the regularization process we use techniques of local zeta functions and embedded resolution of singularities. As an application we present the regularization of p-adic open string amplitudes with Chan-Paton factors and constant B-field. Finally, all the local zeta functions studied here are partition functions of certain 1D log-Coulomb gases, which shows an interesting connection between Koba-Nielsen amplitudes and statistical mechanics.

中文翻译：

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Koba-Nielsen 弦振幅的亚纯延续

在本文中，我们以严格的数学方式确定在特征零的任何局部场上定义的 Koba-Nielsen 振幅是真实积分，允许运动学参数中的亚纯延续。我们的方法使我们能够以统一的方式研究特征零的任意局部场上的开闭 Koba-Nielsen 振幅。在正则化过程中，我们使用局部 zeta 函数和奇点嵌入分辨率的技术。作为一个应用，我们提出了使用 Chan-Paton 因子和恒定 B 场对 p-adic 开弦振幅进行正则化。最后，这里研究的所有局部 zeta 函数都是某些 1D log-Coulomb 气体的配分函数，这表明 Koba-Nielsen 振幅和统计力学之间存在有趣的联系。