Supersymmetric Proof of the Hirzebruch-Riemann-Roch Theorem for   Non-K\"ahler Manifolds
  We present the proof of the HRR theorem for a generic complex compact manifold by evaluating the functional integral for the Witten index of the appropriate supersymmetric quantum mechanical system. 
Andrei V. Smilga
math-ph hep-th math.MP