Crosscaps in Gepner Models and Type IIA Orientifolds

As a first step to a detailed study of orientifolds of Gepner models associated with Calabi-Yau manifolds, we construct crosscap states associated with anti-holomorphic involutions (with fixed points) of Calabi-Yau manifolds. We argue that these orientifolds are dual to M-theory compactifications on (singular) seven-manifolds with $G_2$ holonomy. Using the spacetime picture as well as the M-theory dual, we discuss aspects of the orientifold that should be obtained in the Gepner model. This is illustrated for the case of the quintic.

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