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.
Highlights
In the recent years, scattering amplitudes, considered as mathematical structures, have been studied intensively, see e.g. [3, 26] and the references therein
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
In this article we establish, in a rigorous mathematical way, that the Koba-Nielsen string amplitudes defined on any local field of characteristic zero are bona fide integrals
Summary
In the recent years, scattering amplitudes, considered as mathematical structures, have been studied intensively, see e.g. [3, 26] and the references therein. In this article we establish, in a rigorous mathematical way, that the Koba-Nielsen string amplitudes defined on any local field of characteristic zero are bona fide integrals They admit extensions which are meromorphic complex functions in the kinematic parameters. In [11], it was established in the p-adic setting and by using techniques of Igusa’s local zeta functions that the Koba-Nielsen amplitudes are bona fide integrals. In this article this result is extended to an arbitrary local field of characteristic zero. This is consistent with Volovich’s conjecture asserting that the mathematical description of physical reality must not depend on the background number field, see [55]
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