Feynman Amplitudes and Limits of Heights

Understand

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.