Anomaly cancellation and smooth non-Kähler solutions in heterotic string theory Original Research Article

We show that six-dimensional backgrounds that are image bundle over a Calabi–Yau two-fold base are consistent smooth solutions of heterotic flux compactifications. We emphasize the importance of the anomaly cancellation condition which can only be satisfied if the base is K3 while a image base is excluded. The conditions imposed by anomaly cancellation for the image bundle structure, the dilaton field, and the holomorphic stable bundles are analyzed and the solutions determined. Applying duality, we check the consistency of the anomaly cancellation constraints with those for flux backgrounds of M-theory on eight-manifolds.