On p-adic string amplitudes in the limit p approaches to one

  • M. Bocardo-Gaspar
  • H. García-CompeánEmail author
  • W. A. Zúñiga-Galindo
Open Access
Regular Article - Theoretical Physics


In this article we discuss the limit p approaches to one of tree-level p-adic open string amplitudes and its connections with the topological zeta functions. There is empirical evidence that p-adic strings are related to the ordinary strings in the p → 1 limit. Previously, we established that p-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 p → 1 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 p → 1 of tree-level p-adic string amplitudes give rise to certain amplitudes, that we have named Denef-Loeser string amplitudes. Gerasimov and Shatashvili showed that in limit p → 1 the well-known non-local effective Lagrangian (reproducing the tree-level p-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.


Bosonic Strings Differential and Algebraic Geometry Effective Field Theories 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2018

Authors and Affiliations

  • M. Bocardo-Gaspar
    • 1
  • H. García-Compeán
    • 2
    Email author
  • W. A. Zúñiga-Galindo
    • 1
  1. 1.Departamento de Matemáticas, Unidad Querétaro, Centro de Investigación y de Estudios Avanzados del Instituto Politécnico NacionalSantiago de QuerétaroMéxico
  2. 2.Departamento de Física, Centro de Investigación y de Estudios Avanzados del Instituto Politécnico NacionalMéxicoMéxico

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