A path integral derivation of ${\chi }_y$-genus

Abstract

The formula for the Hirzebruch ${\chi }_y$-genus of complex manifolds is a consequence of the Hirzebruch-Riemann-Roch formula. The classical index formulae for Todd genus, Euler number, and Signature correspond to the case when the complex variable $y=$ 0, -1, and 1 respectively. Here we give a {\it direct} derivation of this nice formula based on supersymmetric quantum mechanics.

5 pages

Cited by in corpus (3)

• A Comment on the chi_y Genus and Supersymmetric Quantum Mechanics
• Supersymmetric Quantum Mechanics and Lefschetz fixed-point formula
• Derivation of Index theorem by Supersymmetry