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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. If the Calabi-Yau threefold has strict SU (3) holonomy then the equations of motion derived from the heterotic string effective action are also satisfied by the solutions we obtain.
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Andreas et al. (2012) studied this question.
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