Superstrings and D-branes in a plane wave

We carefully analyze the supersymmetry algebra of closed strings and open strings in a type IIB plane wave background. We use eight-component chiral spinors, SO(8) chiral spinors, in the light-cone gauge to provide a useful basis for string field theory calculations in a plane wave. We consider the two classes of D-branes, D±-branes, and give a worldsheet derivation of conserved supercurrents for all half Bogomol'nyi-Prasad-Sommerfield (BPS) D-branes preserving 16 supersymmetries in the type IIB plane wave background. We exhaustively provide the supersymmetry algebra of the half BPS branes as well. We also point out that the supersymmetry algebra distinguishes the two SO(4) directions with different signs, which is consistent with the Z2 symmetry of the string action