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

• 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
• 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.

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...