Local Heterotic Torsional Models
  We present a class of smooth supersymmetric heterotic solutions with a non-compact Eguchi-Hanson space. The non-compact geometry is embedded as the base of a six-dimensional non-Kahler manifold with a non-trivial torus fiber. We solve the non-linear anomaly equation in this background exactly. We also define a new charge that detects the non-Kahlerity of our solutions. 
Ji-Xiang Fu, Li-Sheng Tseng, Shing-Tung Yau