Extensions of string theories

With the motivation that critical dimensionsD≠4 might be suggesting that string theories have not been completely formulated, we study more general alternatives. We first consider a direct extension in the world-sheet formulation withN _B bosons andN _F fermions and analyze the conditions for canceling the anomaly in all possible combinations ofN _B ,N _F andD. Later on we incorporate degrees of freedom of antisymmetric tensors to the previous model. The only possibility to cancel the anomaly in this case is withN _B =N _F =1 and the our everyday spacetime dimensionD=4.