We show that six-dimensional backgrounds that are T 2 bundle over a Calabi-Yau twofold 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 T 4 base is excluded. The conditions imposed by anomaly cancellation for the T 2 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.
We construct balanced metrics on the family of non-Kähler Calabi-Yau threefolds that are obtained by smoothing after contracting (−1, −1)-rational curves on a Kähler Calabi-Yau threefold. As an application, we construct balanced metrics on complex manifolds diffeomorphic to the connected sum of k ≥ 2 copies of S 3 × S 3 .
Abstract. In this paper, we generalize the Gauduchon metrics on a compact complex manifold and define the γ k functions on the space of its hermitian metrics.
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