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SIGMA 7 (2011), 105, 14 pages arXiv:1105.3935
https://doi.org/10.3842/SIGMA.2011.105
Dolbeault Complex on S4\{·} and S6\{·} through Supersymmetric Glasses
Andrei V. Smilga
SUBATECH, Université de Nantes, 4 rue Alfred Kastler, BP 20722, Nantes 44307, France
Received June 22, 2011, in final form November 09, 2011; Published online November 15, 2011
Abstract
S4 is not a complex manifold, but it is sufficient to remove one point to make
it complex. Using supersymmetry methods, we show that the Dolbeault complex
(involving the holomorphic exterior derivative ∂ and its Hermitian
conjugate) can be perfectly well defined in this case. We calculate
the spectrum of the Dolbeault Laplacian. It involves 3 bosonic zero modes
such that the Dolbeault index on S4\{·} is equal to 3.
Key words:
Dolbeault; supersymmetry.
pdf (396 kb)
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