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.

Some additional comments were added

References in corpus (7)

• Resolution of singularities for multi-loop integrals
• The massless higher-loop two-point function
• Single-valued integration and superstring amplitudes in genus zero
• p-Adic open string amplitudes with Chan-Paton factors coupled to a constant B-field
• Blowing up Feynman integrals
• 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