Supersymmetric quantum mechanics and topology

Supersymmetric quantum mechanical models are computed by the path integral approach. In the limit, the integrals localize to the zero modes. This allows us to perform the index computations exactly because of supersymmetric localization, and we will show how the geometry of target space enters the physics of sigma models resulting in the relationship between the supersymmetric model and the geometry of the target space in the form of topological invariants. Explicit computation details are given for the Euler characteristics of the target manifold and the index of Dirac operator for the model on a spin manifold.

Note:

26 pages

quantum mechanics: model
operator: Dirac
supersymmetry
geometry
path integral
topological
sigma model
zero mode
topology
spin

References(50)

Figures(0)

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