  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.
