The Strominger system is a system of PDEs derived by Strominger in his study of compactification of heterotic strings with torsion. It can be thought of as a generalization of Ricci-flat metrics on non-Kahler Calabi-Yau 3-folds. We present some new solutions to the Strominger system on a class of noncompact Calabi-Yau 3-folds constructed by twistor technique. These manifolds include the resolved conifold Tot(O(-1,-1)->P^1) as a special case.

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