Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dirac Operator on Complex Manifolds and Supersymmetric Quantum Mechanics   We explore a new simple N=2 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 + \bar Q can be
interpreted as the Dirac operator: the standard Dirac operator if the manifold
is K\"ahler and a certain "truncated" Dirac operator for a generic complex
manifold. Focusing on the K\"ahler 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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The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an