Dolbeault Complex on S^4\{.} and S^6\{.} through Supersymmetric Glasses
Mathematical Physics
2011-11-16 v3 High Energy Physics - Theory
math.MP
Abstract
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.
Cite
@article{arxiv.1105.3935,
title = {Dolbeault Complex on S^4\{.} and S^6\{.} through Supersymmetric Glasses},
author = {Andrei V. Smilga},
journal= {arXiv preprint arXiv:1105.3935},
year = {2011}
}