document: The aim of this note is nothing more than to bring both approaches on equal footing and to relax the assumptions under which the results of [11,13] have been derived using the first approach. More concretely, we generalize the one-loop partition functions, as derived in [11,13] for levels being odd, to the case of even levels. Moreover, on the level of partition functions we implement additional dressings of the world-sheet parity symmetry and identify them with the dressings introduced in [12] in the crosscap state approach. As expected, all the physical information can be read off entirely from the various amplitudes. We will end up with a collection of very explicit and general one-loop partition functions and tadpole cancellation conditions covering simple current extensions of all 168 Gepner models with additional dressings of the parity symmetry. In fact providing a compact collection of the main relevant formulas for constructing supersymmetric Gepner model orientifolds was one of the motivations for writing this Letter. We hope that these expressions turn out to be useful for a systematic search for Standard-like models respectively for providing a statistical ensemble in the spirit of [29].
extractive_keyphrases: bring both approaches on equal footing constructing supersymmetric gepner model orientifolds crosscap state approach current extensions of all 168 gepner models dressings parity symmetry relax the assumptions tadpole cancellation conditions
abstractive_keyphrases: additional dressings of the world-sheet parity symmetry generalize the one-loop partition functions, one-loop partition functions providing a statistical ensemble in the spirit of [29] systematic search for standard-like models