Extended supersymmetries and the Dirac operator
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 s...
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| Veröffentlicht in: | Annals of physics 2005-02, Vol.315 (2), p.467-487 |
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| container_end_page | 487 |
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| container_issue | 2 |
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| container_title | Annals of physics |
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| creator | Kirchberg, A. Länge, J.D. Wipf, A. |
| description | 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 Kähler spaces CPn. |
| doi_str_mv | 10.1016/j.aop.2004.08.006 |
| format | Article |
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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. 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| ispartof | Annals of physics, 2005-02, Vol.315 (2), p.467-487 |
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| subjects | 02.40.Dr 02.40.Ky 11.30.Pb Complex manifolds Dirac operator Kähler manifolds Projective spaces Supersymmetry |
| title | Extended supersymmetries and the Dirac operator |
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