Index Theorems and Supersymmetry
Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
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.
, FYSAST, FYSMAS1019
Aiyah-Singer Index Theorem: Witten Index: Supersymmetric Quantum Mechanics, Path Integrals
Other Physics Topics
IdentifiersURN: urn:nbn:se:uu:diva-237755OAI: oai:DiVA.org:uu-237755DiVA: diva2:768786
Master Programme in Physics
2014-06-02, Uppsala, 13:15 (English)