One loop corrections to coupling constants in String Effective Field Theory

In the framework of a recently proposed method for computing exactly string amplitudes regularized in the infra-red, I determine the one-loop correlators for auxiliary fields in the symmetric $Z_2\times Z_2$ orbifold model. The $D$-field correlation function turns out to give the one-loop corrections for the gauge couplings, which amounts to a string-theory supersymmetry Ward identity. The two-point function for uncharged $F$ fields leads to the one-loop renormalization of the moduli K\"ahler metric, and eventually to the corrections for the Yukawa couplings.