Surviving on the slope: Supersymmetric vacuum in the theories where it is not supposed to be

In supersymmetric models with the run-away vacua or with the stable but non -supersymmetric ground state there exist stable field configurations which restore one half of supersymmetry and are characterized by constant positiv e energy density. We call these solutions "vacua" since they are stable wit h respect to local deformations of the fields. The energy-momentum tensor f or these configurations is proportional to diag{1,-1,-1,0), i.e. they break (spontaneously) the Lorentz and rotational invariances. The formal foundat ion for such vacua is provided by the central extension of the N = 1 supera lgebra with the infinite central charge. (C) 1999 Published by Elsevier Sci ence B.V. All rights reserved.