Extensions of string theories

With the motivation that critical dimensions D≠4 might be suggeting that string theories have not been completely formulated, we study more general alternatives. We first consider a direct extension in the world-sheet formulation with NB bosons and NF fermions and analyze the conditions for canceling the anomaly in all possible combinations of NB, NF and D. 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 with NB=NF=1 and the our everyday spacetime dimension D=4. (orig.)