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Journal Articles International Journal of Modern Physics A Year : 2012

DIRAC OPERATOR ON COMPLEX MANIFOLDS AND SUPERSYMMETRIC QUANTUM MECHANICS

E.A. Ivanov
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A.V. Smilga
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  • IdRef : 115657169

Abstract

We explore a simple N=2 supersymmetric quantum mechanics (SQM) model describing the motion over complex manifolds in external gauge fields. The nilpotent supercharge Q of the model can be interpreted as a (twisted) exterior holomorphic derivative, such that the model realizes the twisted Dolbeault complex. The sum Q+barQ can be interpreted as the Dirac operator: the standard Dirac operator if the manifold is Kähler and the Dirac operator involving certain particular extra torsions for a generic complex manifold. Focusing on the Kähler case, we give new simple physical proofs of the two mathematical facts: (i) the equivalence of the twisted Dirac and twisted Dolbeault complexes and (ii) the Atiyah-Singer theorem.

Dates and versions

in2p3-00906342 , version 1 (19-11-2013)

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Cite

E.A. Ivanov, A.V. Smilga. DIRAC OPERATOR ON COMPLEX MANIFOLDS AND SUPERSYMMETRIC QUANTUM MECHANICS. International Journal of Modern Physics A, 2012, 27, pp.1230024. ⟨10.1142/S0217751X12300244⟩. ⟨in2p3-00906342⟩
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