A path integral derivation of $χ_y$-genus

Details A path integral derivation of $χ_y$-genus A path integral derivation of $χ_y$-genus

2003-06-13

arxiv.org/abs/math-ph/0306041v1

J. Phys. A: Math. Gen. 36(2003) 1083-1086

Physics

Mathematical Physics

5 pages

Scientific paper

10.1088/0305-4470/36/4/315

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.

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