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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2011 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2011
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147990 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862622070888726528 |
|---|---|
| author | Smilga, A.V. |
| author_facet | Smilga, A.V. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-12-07T13:25:53Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147990 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T13:25:53Z |
| publishDate | 2011 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Smilga, A.V. 2019-02-16T12:45:52Z 2019-02-16T12:45:52Z 2011 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. 1815-0659 2010 Mathematics Subject Classification: 32C15; 53B35; 53Z05 http://dx.doi.org/10.3842/SIGMA.2011.105 https://nasplib.isofts.kiev.ua/handle/123456789/147990 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. I am indebted to G. Carron, E. Ivanov, and V. Roubtsov for useful discussions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Dolbeault Complex on S⁴\{·} and S⁶\{·} through Supersymmetric Glasses Article published earlier |
| spellingShingle | Dolbeault Complex on S⁴\{·} and S⁶\{·} through Supersymmetric Glasses Smilga, A.V. |
| title | Dolbeault Complex on S⁴\{·} and S⁶\{·} through Supersymmetric Glasses |
| title_full | Dolbeault Complex on S⁴\{·} and S⁶\{·} through Supersymmetric Glasses |
| title_fullStr | Dolbeault Complex on S⁴\{·} and S⁶\{·} through Supersymmetric Glasses |
| title_full_unstemmed | Dolbeault Complex on S⁴\{·} and S⁶\{·} through Supersymmetric Glasses |
| title_short | Dolbeault Complex on S⁴\{·} and S⁶\{·} through Supersymmetric Glasses |
| title_sort | dolbeault complex on s⁴\{·} and s⁶\{·} through supersymmetric glasses |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147990 |
| work_keys_str_mv | AT smilgaav dolbeaultcomplexons4ands6throughsupersymmetricglasses |