Dolbeault Complex on S^4\{.} and S^6\{.} through Supersymmetric Glasses

Details Dolbeault Complex on S^4\{.} and S^6\{.} through Supersymmetric Glasses Dolbeault Complex on S^4\{.} and S^6\{.} through Supersymmetric Glasses

2011-05-19

arxiv.org/abs/1105.3935v3

SIGMA 7 (2011), 105, 14 pages

Physics

Mathematical Physics

Scientific paper

10.3842/SIGMA.2011.105

S^4 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 S^4\{.} is equal to 3.

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