Derivation of Index theorem by Supersymmetry

Details Derivation of Index theorem by Supersymmetry Derivation of Index theorem by Supersymmetry

2007-01-06

arxiv.org/abs/math-ph/0701018v1

Physics

Mathematical Physics

9 pages

Scientific paper

The present paper gives calculations in detail to prove several special cases
of Atiyah-Singer theorem through supersymmetric $\sigma$-models. Some technical
tricks are employed to calculate the determinants of fluctuation operators of
the path integrals. An intuitive and geometric argument is applied to overcome
the complicated calculation on spin fields twisted by gauge fields.

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