Conical singularities in three or four dimensions and supersymmetry breaking

We present mechanisms for generating conical singularities both in three and four dimensions in the systems with copies of scalar or chiral multiplets coupled to N = 2 or N = 1 supergravity. Our mechanisms are useful for supersymmetry breaking, maintaining the zero cosmological constants in three and four dimensions. A strong coupling duality connecting these two dimensionalities is also studied.