Feynman Amplitudes and Limits of Heights

We investigate from a mathematical perspective how Feynman amplitudes appear in the low-energy limit of string amplitudes. In this paper, we prove the convergence of the integrands. We derive this from results describing the asymptotic behavior of the height pairing between degree-zero divisors, as...

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Bibliographic Details
Published in:arXiv.org 2016-06
Main Authors: Amini, Omid, Bloch, Spencer, Burgos Gil, José I, Fresán, Javier
Format: Article
Language:English
Subjects:
Amplitudes
Asymptotic properties
Riemann surfaces
Online Access:Get full text
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Summary:We investigate from a mathematical perspective how Feynman amplitudes appear in the low-energy limit of string amplitudes. In this paper, we prove the convergence of the integrands. We derive this from results describing the asymptotic behavior of the height pairing between degree-zero divisors, as a family of Riemann surfaces degenerates. These are obtained by means of the nilpotent orbit theorem in Hodge theory.
ISSN:2331-8422
DOI:10.48550/arxiv.1512.04862