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We prove that a given Calabi-Yau threefold with a stable holomorphic vector bundle can be perturbed to a solution of the Strominger system provided that the second Chern class of the vector bundle is equal to the second Chern class of the tangent bundle.
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A. Adams, Conformal field theory and the Reid conjecture, 0703048 [hep-th]
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2007
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J.-X. Fu and S.-T. Yau, The theory of superstring with flux on non-Kähler manifolds and the complex Monge-Ampère, J. Diff. Geom. 78
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M. C. Brambilla, Semistability of certain bundles on a quintic Calabi-Yau threefold, Rev. Mat. Complut. 22
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M. Fernández, S. Ivanov, L. Ugarte, R. Villacampa, Non-Käehler heterotic-string compactifications with non-zero fluxes and constant dilaton, Commun. Math. Phys. 288
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J.-X. Fu, L.-S. Tseng and S.-T. Yau, Local heterotic torsional models, Comm. Math. Phys. 289
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S. Ivanov, Heterotic supersymmetry, anomaly cancellation and equations of motion, Phys. Lett. B 685
2010
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