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DIRAC OPERATOR ON COMPLEX MANIFOLDS AND SUPERSYMMETRIC QUANTUM MECHANICS

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.
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http://hal.in2p3.fr/in2p3-00906342
Contributor : Dominique Girod <>
Submitted on : Tuesday, November 19, 2013 - 3:36:38 PM
Last modification on : Thursday, February 7, 2019 - 5:23:24 PM

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

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