dolbeault complex
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2013 ◽  
Vol 58 (11) ◽  
pp. 1591-1614 ◽  
Author(s):  
D. Fedchenko ◽  
A. Shlapunov


2012 ◽  
Vol 27 (25) ◽  
pp. 1230024 ◽  
Author(s):  
E. A. IVANOV ◽  
A. V. SMILGA

We explore a simple [Formula: see text] 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 [Formula: see text] 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.





Author(s):  
F. COLOMBO ◽  
I. SABADINI ◽  
A. DAMIANO ◽  
D. C. STRUPPA


2008 ◽  
Vol 263 (2) ◽  
pp. 425-445 ◽  
Author(s):  
J. Ruppenthal
Keyword(s):  


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