Dolbeault Complex on S⁴\{·} and S⁶\{·} through Supersymmetric Glasses

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 spectr...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2011
Main Author: Smilga, A.V.
Format: Article
Language:English
Published: Інститут математики НАН України 2011
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/147990
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Dolbeault Complex on S⁴\{·} and S⁶\{·} through Supersymmetric Glasses / A.V. Smilga // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 17 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Summary: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.
ISSN:1815-0659