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In this Part II of D(11), we introduce new objects: super-$C^k$-schemes andAzumaya super-$C^k$-manifolds with a fundamental module (or, synonymously,matrix super-$C^k$-manifolds with a fundamental module), and extend the studyin D(11.1) ([L-Y3], arXiv:1406.0929 [math.DG]) to define the notion of`differentiable maps from an Azumaya/matrix supermanifold with a fundamentalmodule to a real manifold or supermanifold'. This allows us to introduce thenotion of `fermionic D-branes' in two different styles, one parallelsRamond-Neveu-Schwarz fermionic string and the other Green-Schwarz fermionicstring. A more detailed discussion on the Higgs mechanism on dynamical D-branesin our setting, taking maps from the D-brane world-volume to the space-time inquestion and/or sections of the Chan-Paton bundle on the D-brane world-volumeas Higgs fields, is also given for the first time in the D-project. Finallynote that mathematically string theory begins with the notion of adifferentiable map from a string world-sheet (a $2$-manifold) to a targetspace-time (a real manifold). In comparison to this, D(11.1) and the currentD(11.2) together bring us to the same starting point for studying D-branes instring theory as dynamical objects.

D-branes and Azumaya/matrix noncommutative differential geometry,II:  Azumaya/matrix supermanifolds and differentiable maps therefrom -- with a  view toward dynamical fermionic D-branes in string theory