Wess-Zumino actions and Dirichlet Boundary Conditions for Super p-branes with Exotic Fractions of Supersymmetry

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The general solutions in the models of closed and open superstring and super p-branes with exotic fractions of the N=1 supersymmetry are considered and the spontaneously broken character of the OSp(1,2M) symmetry of the models is established. It is shown that extending these models by Wess-Zumino terms generates the Dirichlet boundary conditions for superstring and super p-branes. Using the generalized Wess-Zumino terms new OSp(1,2M) invariant super p-brane and Dp-brane-like actions preserving M-1/M fraction of supersymmetry are proposed. For M=32 these models suggest new superbrane vacua of M-theory preserving 31 from 32 global supersymmetries.