Flavor Symmetries and The Problem of Squark Degeneracy

If supersymmetry exists at low energies, it is necessary to understand why the squark spectrum exhibits sufficient degeneracy to suppress flavor changing neutral currents. In this note, we point out that gauged horizontal symmetries can yield realistic quark mass matrices, while at the same time giving just barely enough squark degeneracy to account for neutral $K$-meson phenomenology. This approach suggests likely patterns for squark masses, and indicates that there could be significant supersymmetric contributions to $B-\bar{B}$ and $D-\bar{D}$ mixing and CP violation in the $K$ and $B$ systems.Comment: preprint SCIPP 93/04,SLAC-PUB-6147, 14 pages, 4 tables included; uses macro package TABLES.TEX and phyzzx forma