Abstract: “I will discuss the one-loop divergence structure of effective field theories from Z3 and Z7 orbifold compactifications of the heterotic string in the U(1)K superspace formalism and its regularization through the use of Pauli-Villars fields.The conformal and chiral anomalies for the two theories are determined in this scheme by matching the chiral anomaly to string calculations. In particular, I will show that the anomaly can be factorized and therefore cancelled by a generalization of the four-dimensional Green-Schwarz mechanism.”