Theory of Superdualities and the Orthosymplectic Supergroup

We study the dualities for sigma models with fermions and bosons. We found that the generalization of the SO(m,m) duality for D=2 sigma models and the Sp(2n) duality for D=4 sigma models is the orthosymplectic duality OSp(m,m|2 n). We study the implications of this and we derive the most general D=2 sigma model, coupled to fermionic and bosonic one-forms, with such dualities. To achieve this we generalize Gaillard-Zumino analysis to orthosymplectic dualities, which requires to define embedding of the superisometry group of the target space into the duality group. We finally discuss the recently proposed fermionic dualities as a by-product of our construction.