Abstract
We investigate the Kähler structure arising inn-component,N=2 supersymmetric quantum mechanics. We defineL 2-cohomology groups of a modified\(\bar \partial \) and relate them to the corresponding spaces of harmonic forms. We prove that the cohomology is concentrated in the middle dimension, and is isomorphic to the direct sum of the local rings of the singularities of the superpotential. In the physics language, this means that the number of ground states is equal to the absolute value of the index of the supercharge, and each ground state contains exactlyn fermions.
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Communicated by A. Jaffe
Supported in part by the Department of Energy under Grant DE-F602-88ER25065
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Klimek, S., Lesniewski, A. Local rings of singularities andN=2 supersymmetric quantum mechanics. Commun.Math. Phys. 136, 327–344 (1991). https://doi.org/10.1007/BF02100028
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DOI: https://doi.org/10.1007/BF02100028