Non-Kaehler Heterotic String Solutions with non-zero fluxes and   non-constant dilaton
  Conformally compact and complete smooth solutions to the Strominger system with non vanishing flux, non-trivial instanton and non-constant dilaton using the first Pontrjagin form of the (-)-connection} on 6-dimensional non-Kaehler nilmanifold are presented. In the conformally compact case the dilaton is determined by the real slices of the elliptic Weierstrass function. The dilaton of non-compact complete solutions is given by the fundamental solution of the Laplacian on $R^4$. 
Marisa Fernandez, Stefan Ivanov, Luis Ugarte, Dimiter vassilev
math.DG hep-th