Discrete torsion in singular G2-manifolds and real LG

Radu Roiban, Christian Römelsberger, Johannes Walcher

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Abstract

We investigate strings at singularities of G2-holonomy manifolds which arise in Z{double-struck}2 orbifolds of Calabi-Yau spaces times a circle. The singularities locally look like R4/Z{double-struck}2 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 J\f = 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.

Original languageEnglish (US)
Pages (from-to)207-278
Number of pages72
JournalAdvances in Theoretical and Mathematical Physics
Volume6
Issue number2
DOIs
StatePublished - Mar 2002

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Physics and Astronomy(all)

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