On \(p\)-adic string amplitudes in the limit \(p\) approaches to one
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Publication:1783786
DOI10.1007/JHEP08(2018)043zbMATH Open1396.83044arXiv1712.08725OpenAlexW3101525300MaRDI QIDQ1783786
Author name not available (Why is that?)
Publication date: 21 September 2018
Published in: (Search for Journal in Brave)
Abstract: In this article we discuss the limit approaches to one of tree-level -adic open string amplitudes and its connections with the topological zeta functions. There is empirical evidence that -adic strings are related to the ordinary strings in the limit. Previously, we established that -adic Koba-Nielsen string amplitudes are finite sums of multivariate Igusa's local zeta functions, consequently, they are convergent integrals that admit meromorphic continuations as rational functions. The meromorphic continuation of local zeta functions has been used for several authors to regularize parametric Feynman amplitudes in field and string theories. Denef and Loeser established that the limit of a Igusa's local zeta function gives rise to an object called topological zeta function. By using Denef-Loeser's theory of topological zeta functions, we show that limit of tree-level -adic string amplitudes give rise to certain amplitudes, that we have named Denef-Loeser string amplitudes. Gerasimov and Shatashvili showed that in limit the well-known non-local effective Lagrangian (reproducing the tree-level -adic string amplitudes) gives rise to a simple Lagrangian with a logarithmic potential. We show that the Feynman amplitudes of this last Lagrangian are precisely the amplitudes introduced here. Finally, the amplitudes for four and five points are computed explicitly.
Full work available at URL: https://arxiv.org/abs/1712.08725
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