科研之友
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摘要
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 + (Q) over bar can be interpreted as the Dirac operator: the standard Dirac operator if the manifold is Kahler and the Dirac operator involving certain particular extra torsions for a generic complex manifold. Focusing on the Kahler 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.
- 出版日期2012-10-10
