Solvable N = (4, 4) type IIA string theory in plane-wave background and D-branes

We study various aspects of N = (4, 4) type IIA GS superstring theory in the pp-wave background, which arises as the compactification of maximally supersymmetric eleven-dimensional pp-wave geometry along the spacelike isometry direction.We show the supersymmetry algebra of N = (4, 4) worldsheet supersymmetry as well as non-linearly realized supersymmetry. We also give quantization of closed string and open string incorporating various boundary conditions. From the open string boundary conditions, we find configurations of D-branes which preserve half the supersymmetries. Among these we identify D4-brane configurations with longitudinal five-brane configurations in matrix model on the eleven-dimensional pp-wave geometry.