Spectral Bundles and the DRY-Conjecture

TL;DR

This paper confirms a version of the DRY-Conjecture by showing that certain fivebrane classes in heterotic string models can be realized as stable bundles, providing an alternative to fivebrane inclusion for anomaly cancellation.

Contribution

It establishes a sufficient condition for fivebrane classes to be realized as stable bundles, confirming a specific case of the DRY-Conjecture in heterotic string theory.

Findings

Certain cohomology classes can be realized as stable bundles.

The sufficient condition for fivebrane classes is satisfied.

Existence of bundles realizing these classes is proven.

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.