Strings in a PP-wave background compactified on T⁸ with twisted S¹

We study a torus-like compactification of type IIB maximally supersymmetric PP-wave background. As the most general case, we discuss a T^8 compactification of all the transverse directions. A nontrivial structure of the isometry group requires an additional light-like compactification. This additional S^1 fiber is twisted on the T^8. We determine the spectrum of closed strings in this twisted torus background and compute the thermal partition function.