Axion Couplings and Effective Cut-Offs in Superstring Compactifications
  We use the linear supermultiplet formalism of supergravity to study axion couplings and chiral anomalies in the context of field-theoretical Lagrangians describing orbifold compactifications beyond the classical approximation. By matching amplitudes computed in the effective low energy theory with the results of string loop calculations we determine the appropriate counterterm in this effective theory that assures modular invariance to all loop order. We use supersymmetry consistency constraints to identify the correct ultra-violet cut-offs for the effective low energy theory. Our results have a simple interpretation in terms of two-loop unification of gauge coupling constants at the string scale. 
Mary K. Gaillard and T.R. Taylor