New and Strong Constraints on the Parameter Space of the MSSM from Charge and Color Breaking Directions

Although the possible existence of dangerous charge and color breaking (CCB) directions in the MSSM has been known since the early 80's, only particular directions in the field-space have been considered, thus obtaining necessary but not sufficient conditions to avoid dangerous CCB minima. Furthermore, the radiative corrections to the potential were not normally included in a proper way, often leading to an overestimation of the restrictive power of the bounds. It turns out that when correctly evaluated, the ``traditional" CCB bounds are very weak. I give here a brief survey of recent results on this subject, which represent a complete analysis, showing that the new CCB bounds are very strong and, in fact, there are extensive regions in the parameter space that become forbidden. This produces important bounds, not only on the value of $A$, but also on the values of $B$ and $M_{1/2}$. The form of strongest one of the new bounds, the so called UFB-3 bound, is explicitely given.