A Note on Moduli Stabilisation in Heterotic Models in the Presence of   Matter Fields
  In this brief note we analyse a toy model which can be derived from heterotic string compactifications on half-flat manifolds with SU(3) structure at first order in \alpha' (ie including matter fields). We show that for this model, finding solutions with viable gauge group poses the same problems as finding solutions in the absence of matter fields. 
Andrei Micu