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We consider Neveu-Schwarz pp-waves with spacetime supersymmetry. Uponcompactification of a spacelike direction, these backgrounds develop ClosedNull Curves (CNCs) and Closed Timelike Curves (CTCs), and are U-dual tosupersymmetric Godel type universes. We study classical and quantum strings inthis background, with emphasis on the strings winding around the compactdirection. We consider two types of strings: long strings stabilized by NS fluxand rotating strings which are stabilized against collapse by angular momentum.Some of the latter strings wrap around CNCs and CTCs, and are thus a potentialsource of pathology. We analyze the partition function, and in particulardiscuss the effects of these string states. Although our results are notconclusive, the partition function seems to be dramatically altered due to thepresence of CNCs and CTCs. We discuss some interpretations of our results,including a possible sign of unitary violation.Comment: 42 pages, LaTeX, 2 figure

Classical and quantum strings in compactifiedppwaves and Gödel type universes