2002/03/31 by Radu Roiban, Christian Romelsberger, Johannes Walcher
Physics and Astronomy · #hep-th
published as Adv.Theor.Math.Phys. 6 (2003) 207-278 · 71 pages, 4 figures, refs added, signs fixed
arxiv created 2003/12/26 · arxiv updated 2009/11/30
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 R4/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 Calabi-Yau 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.