Feynman Amplitudes and Limits of Heights
Algebraic Geometry
2016-11-01 v2 Mathematical Physics
math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.1512.04862,
title = {Feynman Amplitudes and Limits of Heights},
author = {Omid Amini and Spencer Bloch and José I. Burgos Gil and Javier Fresán},
journal= {arXiv preprint arXiv:1512.04862},
year = {2016}
}
Comments
Final version, 44 pages. To appear in Izvestiya: Mathematics, special volume in honor of Jean-Pierre Serre