p-Adic open string amplitudes with Chan-Paton factors coupled to a constant B-field

Abstract

We establish rigorously the regularization of the p-adic open string amplitudes, with Chan-Paton rules and a constant B-field, introduced by Ghoshal and Kawano. In this study we use techniques of multivariate local zeta functions depending on multiplicative characters and a phase factor which involves an antisymmetric bilinear form. These local zeta functions are new mathematical objects. We attach to each amplitude a multivariate local zeta function depending on the kinematics parameters, the B-field and the Chan-Paton factors. We show that these integrals admit meromorphic continuations in the kinematic parameters, this result allows us to regularize the Goshal-Kawano amplitudes, the regularized amplitudes do not have ultraviolet divergences. Due to the need of a certain symmetry, the theory works only for prime numbers which are congruent to 3 modulo 4. We also discuss the limit p tends to 1 in the noncommutative effective field theory and in the Ghoshal-Kawano amplitudes. We show that in the case of four points, the limit p tends to 1 of the regularized Ghoshal-Kawano amplitudes coincides with the Feynman amplitudes attached to the limit p tends to 1 of the noncommutative Gerasimov-Shatashvili Lagrangian.

arXiv commentThe notation was simplified, and some calculations were shortened

References in corpus (25)

• String Theory and Noncommutative Geometry
• Noncommutative Perturbative Dynamics
• On Background Independent Open-String Field Theory
• On Exact Tachyon Potential in Open String Field Theory
• Noncommutative ${\Phi }^4$ Theory at Two Loops
• $p$-Adic Mathematical Physics: The First 30 Years
• $p$-adic AdS/CFT
• Edge length dynamics on graphs with applications to $p$-adic AdS/CFT
• Holographic dual of the five-point conformal block
• On the relation between p-adic and ordinary strings
• Signs of the time: Melonic theories over diverse number systems
• Towards p-Adic String in Constant B-Field
• Tensor networks, $p$-adic fields, and algebraic curves: arithmetic and the AdS${}_3$/CFT${}_2$ correspondence
• On the Exchange Interactions in Holographic p-adic CFT
• Spin in $p$-adic AdS/CFT
• Exact noncommutative solitons in p-adic strings and BSFT
• Meromorphic Continuation of Koba-Nielsen String Amplitudes
• Deformation of p-adic String Amplitudes in a Magnetic Field
• Acausal quantum theory for non-Archimedean scalar fields
• Non-Archimedean Replicator Dynamics and Eigen's Paradox
• Building Archimedean Space
• Reaction-diffusion Equations on Complex Networks and Turing Patterns, via p-Adic Analysis
• General relativity from $p$-adic strings
• p-adic CFT is a holographic tensor network
• Nonarchimedean Holographic Entropy from Networks of Perfect Tensors

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• Euclidean Quantum Field Formulation of p-Adic open string amplitudes
• Plahte Diagrams for String Scattering Amplitudes
• Emergent quantum mechanics of the event-universe, quantization of events via Denrographic Hologram Theory
• Towards Non-archimedean Superstrings
• From $p$-adic to Archimedean Physics: Renormalization Group Flow and Berkovich Spaces
• Finite Temperature at Finite Places
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