The Abelian Heterotic Conifold
  We study heterotic supergravity on the conifold and its Z2 orbifold with Abelian gauge fields and three-form flux. At large distances, these solutions are locally Ricci-flat, have a magnetic flux through the two-sphere at infinity as well as non-zero five-brane charge. For a given flux, our family of solutions has three real parameters, the size of the pair of two spheres in the IR and the dilaton zero mode. We present an explicit analytic solution for the decoupled near horizon region where for a given flux, the size of the cycles is frozen and the only parameter is the dilaton zero mode. We also present an exactly solvable worldsheet CFT for this near horizon region. When one of the two cycles has vanishing size, the near horizon region no longer exists but we obtain a solution on the (unorbifolded) resolved conifold. 
Nick Halmagyi, Dan Israel, Eirik Eik Svanes
hep-th