Abstract
In tensor products of a left-right symmetric CFT, one can define permutation orientifolds by combining orientation reversal with involutive permutation symmetries. We construct the corresponding crosscap states in general rational CFTs and their orbifolds, and study in detail those in products of affine U(1)2 models or N = 2 minimal models. The results are used to construct permutation orientifolds of Gepner models. We list the permutation orientifolds in a few simple Gepner models, and study some of their physical properties — supersymmetry, tension and RR charges. We also study the action of corresponding parity on D-branes, and determine the gauge group on a stack of parity-invariant D-branes. Tadpole cancellation condition and some of its solutions are also presented.
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