Minimal Supersymmetric $SU(4) \times SU(2)_L \times SU(2)_R$

We present a minimal string-inspired supersymmetric $SU(4) \times SU(2)_L \times SU(2)_R$ model, and provide a detailed analysis of the symmetry breaking potential in this model, based on a generalisation of that recently proposed by Dvali, Lazarides and Shafi. The model contains a global U(1) R-symmetry and reduces to the MSSM at low energies. However it improves on the MSSM since it explains the magnitude of its $\mu$ term and gives a prediction for $\tan \beta \simeq m_t/m_b$. It also predicts an essentially stable proton, and contains both `cold' and `hot' dark matter candidates. A period of hybrid inflation above the symmetry breaking scale is also possible in this model. Finally it suggests the existence of `heavy' charge $\pm e/6$ (colored) and $\pm e/2$ (color singlet) states.