On the Evaluation of Compton Scattering Amplitudes in String Theory

TL;DR

This paper computes the one-loop Compton scattering amplitude in a four-dimensional heterotic string model, detailing the derivation from world-sheet fermion bosonization to the integral over modular forms.

Contribution

It provides an explicit calculation of the Compton amplitude at genus one in a fermionic heterotic string, including the detailed steps of world-sheet fermion bosonization.

Findings

Explicit form of the one-loop Compton amplitude derived

Integral representation over modular forms obtained

Methodology for similar amplitude calculations established

Abstract

We consider the Compton amplitude for the scattering of a photon and a (massless) ``electron/positron'' at one loop (i.e. genus one) in a four-dimensional fermionic heterotic string model. Starting from the bosonization of the world-sheet fermions needed to explicitly construct the spin-fields representing the space-time fermions, we present all the steps of the computation which leads to the explicit form of the amplitude as an integral of modular forms over the moduli space.