Green-Schwarz Anomaly Cancellation, World Sheet Instantons and Wormholes

We consider the breaking of the global conservation of gauge field charges which are commonly thought to survive the spontaneous breakdown of gauge symmetry brought about by Kalb-Ramond fields. Depending on the dilaton field and also the size of the compactifying space, the global charge breaking may take place due to world sheet instantons. In going to 3+1 dimensions one could have a serious problem in order to produce the hierarchies between the quark and the charged lepton masses using the mass protecting charges with the Green-Schwartz anomaly cancellation. Various unnatural features of this type of models are discussed.