Crosscaps in Gepner Models and the Moduli space of T2 Orientifolds

TL;DR

This paper explores the moduli space of T^2 orientifolds using geometrical and conformal field theory methods, deriving orientifold plane charges and extending insights to elliptically fibered K3 surfaces.

Contribution

It provides a detailed comparison between geometric involutions and CFT results in Gepner models, introducing new crosscap coefficients and linking to mathematical theories of elliptic curves.

Findings

Derived the moduli space of orientifolded T^2s using involutive automorphisms.

Constructed half-supersymmetry preserving crosscap coefficients for Gepner models.

Connected orientifold plane charges to fixed points of involutions and mathematical properties of elliptic curves.

Abstract

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^2s. 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^2s 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.