Meromorphic Continuation of Koba-Nielsen String Amplitudes

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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References in corpus (19)

• String Theory and Noncommutative Geometry
• Motivic Igusa zeta functions
• Resolution of singularities for multi-loop integrals
• The massless higher-loop two-point function
• Single-valued integration and superstring amplitudes in genus zero
• From elliptic multiple zeta values to modular graph functions: open and closed strings at one loop
• Periods and Feynman integrals
• p-Adic open string amplitudes with Chan-Paton factors coupled to a constant B-field
• Towards p-Adic String in Constant B-Field
• Single-valued hyperlogarithms, correlation functions and closed string amplitudes
• Blowing up Feynman integrals
• Free-field realisation of boundary states and boundary correlation functions of minimal models
• Coulomb-gas approach for boundary conformal field theory
• Exact noncommutative solitons in p-adic strings and BSFT
• Deformation of p-adic String Amplitudes in a Magnetic Field
• Acausal quantum theory for non-Archimedean scalar fields
• On $p$-adic string amplitudes in the limit $p$ approaches to one
• Graphs, local zeta functions, Log-Coulomb Gases, and phase transitions at finite temperature
• The boundary states and correlation functions of the tricritical Ising model from the Coulomb-gas formalism

Cited by in corpus (10)

• p-Adic open string amplitudes with Chan-Paton factors coupled to a constant B-field
• p-Adic Statistical Field Theory and Deep Belief Networks
• Euclidean Quantum Field Formulation of p-Adic open string amplitudes
• Non-Archimedean Quantum Mechanics via Quantum Groups
• Plahte Diagrams for String Scattering Amplitudes
• Towards Non-archimedean Superstrings
• Archimedean Zeta Functions and Oscillatory Integrals
• Closed form expression for the 5-point Veneziano amplitude in terms of 4-point amplitudes
• Local Zeta Functions and Koba-Nielsen String Amplitudes
• Massless $p2$-brane modes and the critical line