Yukawa textures in string unified models withSU(4)⊗O(4)symmetry

We discuss the origin of Yukawa textures in the string-inspired and string-derived models based on the gauge group $\mathrm{SU}\mathrm{}\left(4\right)\mathrm{}\otimes \mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_L\otimes \mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_R$ supplemented by a $\mathrm{U}{\mathrm{}\left(1\right)\mathrm{}}_X$ gauged family symmetry. The gauge symmetries are broken down to those of the minimal supersymmetric standard model which is the effective theory below ${10}^{16}$ GeV. The combination of the $\mathrm{U}{\mathrm{}\left(1\right)\mathrm{}}_X$ family symmetry and the Pati-Salam gauge group leads to a successful and predictive set of Yukawa textures involving two kinds of texture zeros: horizontal and vertical texture zeros. We discuss both symmetric and nonsymmetric textures in models of this kind, and in the second case perform a detailed numerical fit to the charged fermion mass and mixing data. Two of the Yukawa textures allow a low energy fit to the data with a total ${\chi }^2$ of 0.39 and 1.02, respectively, for three degrees of freedom. We also make a first attempt at deriving the nonrenormalizable operators required for the Yukawa textures from string theory.