Heterotic string covariant amplitudes and low-energy effective action

Abstract

We compute the 3- and 4-point scattering amplitudes for gravitons, antisymmetric tensors, and gauge bosons in the heterotic string model using the covariant path integral formalism. From these amplitudes we deduce all the terms in the low-energy effective action involving cubic and quartic interactions of those fields, that are not affected by pole subtractions. We show that the spin connection should naturally contain torsion whose sign is unambiguously determined by the string amplitudes. The quartic interactions arising from the pure heterotic string part of the amplitudes (i.e. the pieces which are not contained in the SST-scattering amplitudes) are shown to vanish when the gauge field is embedded in the spin connection with torsion ( A μ → ω μ ). Some consequences for compactification are discussed.