Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 8 (2012), 003, 12 pages      arXiv:1109.2867      https://doi.org/10.3842/SIGMA.2012.003

Supersymmetric Proof of the Hirzebruch-Riemann-Roch Theorem for Non-Kähler Manifolds

Andrei V. Smilga
SUBATECH, Université de Nantes, 4 rue Alfred Kastler, BP 20722, Nantes 44307, France

Received November 10, 2011, in final form January 04, 2012; Published online January 08, 2012

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.

Key words: index; Dolbeault; supersymmetry.

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