Crosscaps in Gepner Models and the Moduli space of T 2 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 ’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 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. Email addresses: [email protected], [email protected], [email protected] ∗ Current address.