Extended Supersymmetries and the Dirac Operator

Details Extended Supersymmetries and the Dirac Operator Extended Supersymmetries and the Dirac Operator

2004-01-20

arxiv.org/abs/hep-th/0401134v2

Annals Phys. 315 (2005) 467-487

Physics

High Energy Physics

High Energy Physics - Theory

22 pages, no figures

Scientific paper

10.1016/j.aop.2004.08.006

We consider supersymmetric quantum mechanical systems in arbitrary dimensions on curved spaces with nontrivial gauge fields. The square of the Dirac operator serves as Hamiltonian. We derive a relation between the number of supercharges that exist and restrictions on the geometry of the underlying spaces as well as the admissible gauge field configurations. From the superalgebra with two or more real supercharges we infer the existence of integrability conditions and obtain a corresponding superpotential. This potential can be used to deform the supercharges and to determine zero modes of the Dirac operator. The general results are applied to the Kahler spaces CP^n.

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