Feynman Amplitudes and Limits of Heights
arXiv:1512.04862 · doi:10.1070/IM8492
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.
Final version, 44 pages. To appear in Izvestiya: Mathematics, special volume in honor of Jean-Pierre Serre