Abstract
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.
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ArXiv ePrint: 1905.10879
The second author was supported by KU Leuven grant C14/17/083. The third author was partially supported by Conacyt Grant No. 250845.
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Bocardo-Gaspar, M., Veys, W. & Zúñiga-Galindo, W.A. Meromorphic continuation of Koba-Nielsen string amplitudes. J. High Energ. Phys. 2020, 138 (2020). https://doi.org/10.1007/JHEP09(2020)138
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DOI: https://doi.org/10.1007/JHEP09(2020)138