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Index Theorems and Supersymmetry
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
2014 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

The Atiyah-Singer index theorem, the Euler number, and the Hirzebruch signature are derived via the supersymmetric path integral. Concisely, the supersymmetric path integral is a combination of a bosonic and a femionic path integral. The action in the supersymmetric path integral includes here bosonic, fermionic- and isospin fields (backgroundfields), where the cross terms in the Lagrangian are nicely eliminated due to scaling of the fields and using techniques from spontaneous breaking of supersymmetry (that give rise to a mechanism, analogous to the Higgs-mechanism, but here regarding the so called superparticles instead).  Thus, the supersymmetric path integral is a product of three pathintegrals over the three given fields, respectively, that can be evaluated exactly by means of Gaussian integrals. The closely related Witten index is a measure of the failure of spontaneous breaking of supersymmetry. In addition, the basic concepts of supersymmetry breaking are reviewed.

Place, publisher, year, edition, pages
2014. , 75 p.
Keyword [en]
Aiyah-Singer Index Theorem: Witten Index: Supersymmetric Quantum Mechanics, Path Integrals
National Category
Other Physics Topics
URN: urn:nbn:se:uu:diva-237755OAI: diva2:768786
Educational program
Master Programme in Physics
2014-06-02, Uppsala, 13:15 (English)
Available from: 2015-02-20 Created: 2014-12-04 Last updated: 2015-02-20Bibliographically approved

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