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.Comment: 5 page