Supersymmetric Proof of the Hirzebruch-Riemann-Roch Theorem for Non-Kähler Manifolds - Smilga, A.V. (Symmetry, Integrability and Geometry: Methods and Applications, 2012)
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.