Abstract : 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.
A.V. Smilga. Supersymmetric Proof of the Hirzebruch-Riemann-Roch Theorem for Non-Kähler Manifolds. Symmetry, Integrability and Geometry : Methods and Applications, National Academy of Science of Ukraine, 2012, 8, pp.003. <10.3842/SIGMA.2012.003>. <in2p3-00667200>