String κ-anomalies and D = 10 supergravity constraints: the solution of a puzzle

The κ-anomaly cancellation mechanism in the heterotic superstring determines the superspace constraints for N = 1, D = 10 Supergravity-Super-Yang-Mills theory. We point out that the constraints found recently in this way appear to disagree with superspace solutions found in the past. We solve this puzzle establishing perfect agreement between the two methods.