Discrete torsion in singular $G_2$-manifolds and real LG

Abstract

We investigate strings at singularities of G2-holonomy manifolds which arise in Z2 orbifolds of Calabi-Yau spaces times a circle. The singularities locally look like R 4 /Z2 fibered over a SLAG, and can globally be embedded in CICYs in weighted projective spaces. The local model depends on the choice of a discrete torsion in the fibration, and the global model on an anti-holomorphic involution of the CalabiYau hypersurface. We determine how these choices are related to each other by computing a Wilson surface detecting discrete torsion. We then follow the same orbifolds to the non-geometric Landau-Ginzburg region of moduli space. We argue that the symmetry-breaking twisted sectors are effectively captured by real Landau-Ginzburg potentials. In particular, we find agreement in the low-energy spectra of strings computed from geometry and Gepner-model CFT. Along the way, we construct the full modular data of orbifolds of N = 2 minimal models by the mirror automorphism, and give a real-LG interpretation of their modular invariants. Some of the models provide examples of the mirror-symmetry phenomenon for G2 holonomy. e-print archive: http://lanl.arXiv.org/abs/hep-th/0203272