Superstring at the boundary of open supermembrane interacting with D=4 supergravity and matter supermultiplets

We present the complete supersymmetric and $\kappa$--symmetric action for the 4-dimensional interacting system of open supermembrane, dynamical supergravity and 3--form matter multiplets. The cases of a single 3-form matter multiplet and a quite generic model with a number of nonlinear interacting double 3-form multiplets are considered. In all cases the fermionic parameter of the $\kappa$-symmetry is subject to two apparently different projection conditions which suggests that the ground state of the system, in particular a domain junction, might preserve at most 1/4 of the spacetime supersymmetry. The boundary term of the open supermembrane action, needed to preserve the $\kappa$-symmetry, has the meaning of the action of a superstring. The Wess--Zumino term of this superstring action is expressed in terms of real linear superfield playing the role of St\"uckelberg field for the 3--form gauge symmetry. This indicates that this symmetry is broken spontaneously by the superstring at the boundary of supermembrane.