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arXiv · 1010.1644

On possible Chern Classes of stable Bundles on Calabi-Yau threefolds

Bjorn Andreas·Gottfried Curio
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Abstract

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 $c_2(V)$ and $c_2(X)$; 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 $c_2(V)$ is of a certain form. In this note we prove that on elliptically fibered $X$ infinitely many cohomology classes $c\in H^4(X, {\bf Z})$ exist which are of this form and for each of them a stable SU(n) vector bundle with $c=c_2(V)$ exists.

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Bjorn Andreas, Gottfried Curio. 2010-10-08. On possible Chern Classes of stable Bundles on Calabi-Yau threefolds. https://doi.org/10.1016/j.geomphys.2011.03.001

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