Spectral Bundles and the DRY-Conjecture

Abstract: Supersymmetric heterotic string models, built from a Calabi-Yau threefold $X$ endowed with a stable vector bundle $V$, usually start from a phenomenologically motivated choice of a bundle $V_v$ in the visible sector, the spectral cover construction on an elliptically fibered $X$ being a prominent example. The ensuing anomaly mismatch between $c_2(V_v)$ and $c_2(X)$, or rather the corresponding differential forms, is often 'solved', on the cohomological level, by including a fivebrane. This leads to the question whether the difference can be alternatively realized by a further stable bundle. The 'DRY'-conjecture of Douglas, Reinbacher and Yau in math.AG/0604597 gives a sufficient condition on cohomology classes on $X$ to be realized as the Chern classes of a stable sheaf. In arXiv:1010.1644 we showed that infinitely many classes on $X$ exist for which the conjecture ist true. In this note we give the sufficient condition for the mentioned fivebrane classes to be realized by a further stable bundle in the hidden sector. Using a result obtained in arXiv:1011.6246 we show that corresponding bundles exist, thereby confirming this version of the DRY-Conjecture.