It is shown that a double compactified $D=11\mathrm{}$ supermembrane with nontrivial wrapping may be formulated as a symplectic noncommutative gauge theory on the world volume. The symplectic noncommutative structure is intrinsically obtained from the symplectic two-form on the world volume defined by the minimal configuration of its Hamiltonian. The gauge transformations on the symplectic fibration are generated by the area preserving diffeomorphisms on the world volume. Geometrically, this gauge theory corresponds to a symplectic fibration over a compact Riemann surface with a symplectic connection.

• Received 30 January 2001

DOI:https://doi.org/10.1103/PhysRevD.64.046001