and anticommutators is explained in detail in Refs. [@Ortin:2002qb; @Alonso-Alberca:2002dw] and the consistency of the scheme was proven in [@Figueroa-O'Farrill:2004mx]. According to the Kaluza-Klein principle we enunciated at the beginning, conveniently generalized to the supersymmetric case, this global supersymmetry algebra becomes the algebra of the local symmetries of the field theories constructed on this field configuration.

Of course, we do not want to construct field theories on just any field configuration but only on vacua of the theory. In general, for a field configuration to be considered a vacuum, we require that it is a classical solution of the equations of motion of the theory. Apart from this requirement, it is not clear what *a priori* characteristics a good vacuum must have except for classical and quantum stability, which are difficult to test in general, but which are, under certain conditions, guaranteed by the presence of unbroken supersymmetry. This is one of the reasons that makes supersymmetric vacua interesting. We also *prefer* highly symmetric vacua (such as Minkowski or anti-De Sitter space) since, on them, we can define a large number of conserved quantities, but it is uncertain why Nature should have the same prejudices.

Sometimes, when a vacuum solution 