On the heterotic effective action at one-loop, gauge couplings and the gravitational sector

We present in detail the procedure for calculating the heterotic one-loop effective action. We focus on gravitational and gauge couplings. We show that the two-derivative couplings of the gravitational sector are not renormalized at one loop when the ground state is supersymmetric. Arguments are presented that this non-renormalization theorem persists to all orders in perturbation theory. Arguments are presented that this non-renormalization theorem persists to all orders in perturbation theory. We also derive the full one-loop correction to the gauge coupling. For a class of N=2 ground states, namely those that are obtained by toroidal compactification to four dimensions of generic six-dimensional N=1 models, we give an explicit formula for the gauge-group independent thresholds, and show that these are equal within the whole family.