Charge and Color Breaking in Supersymmetry and Superstring

Charge and color breaking minima in SUSY theories might make the standard vacuum unstable. In this talk a brief review of this issue is performed. When a complete analysis of all the potentially dangerous directions in the field space of the theory is carried out, imposing that the standard vacuum should be the global minimum, the corresponding constraints turn out to be very strong and, in fact, there are extensive regions in the parameter space of soft SUSY–breaking terms that become forbidden. For instance, in the context of the MSSM with universal soft terms, this produces important bounds, not only on the value of A, but also on the values of B, M and m. In specific SUSY scenarios, as fixed point models, no–scale supergravity, gauge–mediated SUSY breaking and superstrings, the charge and color breaking constraints are also very important. For example, if the dilaton is the source of SUSY breaking in four–dimensional superstrings, the whole parameter space (m3/2,B) is excluded on these grounds. Cosmological analyses are also briefly reviewed. 1 Based on talks given at ‘Beyond the desert: accelerator and non–accelerator approaches’, Castle Ringberg, Tegernsee (Germany), June 1997; ‘8th Miniworkshop on Particle and Astroparticle Physics’, Pusan (South Korea), May 1997. 2 Permanent address: Departamento de F́ısica Teórica, Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid, Spain.