Yukawa Textures and Anomalies

We augment the Minimal Supersymmetric Standard Model with a gauged family-dependent $U(1)$ to reproduce Yukawa textures compatible with experiment. In the simplest model with one extra chiral electroweak singlet field, acceptable textures require this $U(1)$ to be anomalous. The cancellation of its anomalies by a generic Green-Schwarz mechanism requires ${\sin }^2{\theta }_w=3\mathrm{/}8$ at the string scale, suggesting a superstring origin for the standard model.