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Advances in High Energy Physics
Volume 2016 (2016), Article ID 3906746, 10 pages
Review Article

Supersymmetric Quantum Mechanics and Topology

Department of Physics, University of Agriculture, Faisalabad 38040, Pakistan

Received 11 November 2015; Revised 21 January 2016; Accepted 4 February 2016

Academic Editor: Elias C. Vagenas

Copyright © 2016 Muhammad Abdul Wasay. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.


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.