Crosscaps in Gepner models and the moduli space of T2 orientifolds

We study T-2 orientifolds and their moduli space in detail. Geometrical insight into the involutive automorphisms of T-2 allows a straightforward derivation of the moduli space of orientifolded T(2)s. Using c = 3 Gepner models, we compare the explicit worldsheet sigma model of an orientifolded T-2 compactification with the CFT results. In doing so, we derive half-supersymmetry preserving crosscap coefficients for generic unoriented Gepner models using simple current techniques to construct the charges and tensions of Calabi-Yau orientifold planes. For T(2)s, we are able to identify the O-plane charge directly as the number of fixed points of the involution; this number plays an important role throughout our analysis. At several points we make connections with the mathematical literature on real elliptic curves. We conclude with a preliminary extension of these results to elliptically fibered K3s.