Plane Wave Type II${}^{\ast }$ String Backgrounds

In this note we aim to study plane-wave limits of the solutions of type II${}^{\ast }$ superstring theories. We consider Freund-Rubin type $d{S}_5\times H^5$ solutions of type IIB${}^{\ast }$ theory and obtain a new kind of plane-wave solutions, we refer them as de Sitter plane-waves or Dpp-waves. Considering Hull’s time-like T-duality we are able to map the Dpp wave solution to maximally supersymmetric Hpp-wave in IIB string theory and vice-versa.