D-branes on Calabi-Yau Manifolds and Superpotentials
  We show how to compute terms in an expansion of the world-volume superpotential for fairly general D-branes on the quintic Calabi-Yau using linear sigma model techniques, and show in examples that this superpotential captures the geometry and obstruction theory of bundles and sheaves on this Calabi-Yau. 
Michael R. Douglas (Rutgers/IHES/INI), Suresh Govindarajan (IIT   Chennai), T. Jayaraman (IMSc) and Alessandro Tomasiello (C...