2010/10/31 by Bjorn Andreas, Gottfried Curio · 1 citation
Physics and Astronomy · Mathematics · #hep-th #math.AG
paper · pdf · doi:10.1016/j.geomphys.2011.03.001
published as J.Geom.Phys.61:1378-1384,2011 · 12 pages latex, minor changes
arxiv created 2010/12/17 · arxiv updated 2011/05/25
Supersymmetric heterotic string models, built from a Calabi-Yau threefold X endowed with a stable vector bundle V, usually lead to an anomaly mismatch between c2(V) and c2(X); this leads to the question whether the difference can be realized by a further bundle in the hidden sector. In math.AG/0604597 a conjecture is stated which gives sufficient conditions on cohomology classes on X to be realized as the Chern classes of a stable reflexive sheaf V; a weak version of this conjecture predicts the existence of such a V if c2(V) is of a certain form. In this note we prove that on elliptically fibered X infinitely many cohomology classes c∈ H4(X, \bf Z) exist which are of this form and for each of them a stable SU(n) vector bundle with c=c2(V) exists.