No pair production of open strings in a plane-wave background

We consider whether an external electric field may cause the pair production of open strings in a type IIA plane-wave background. The boundary states of D-branes with condensates are constructed in the Green-Schwarz formulation of superstring theory with the light-cone gauge. The cylinder diagrams are computed with massive theta functions. Although the value of the electric field is bounded by the upper value, there is no pole in the amplitudes and it indicates that no pair production occurs in the plane-wave background. This result would be universal for a class of plane-wave backgrounds.