Dolbeault Complex on S^4{·} and S^6{·} through Supersymmetric Glasses
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 spect...
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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2011-11-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Online Access: | http://dx.doi.org/10.3842/SIGMA.2011.105 |
| _version_ | 1818346415607250944 |
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| author | Andrei V. Smilga |
| author_facet | Andrei V. Smilga |
| author_sort | Andrei V. Smilga |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-13T17:17:54Z |
| format | Article |
| id | doaj.art-5afaf0892fc44919816f3633d2288027 |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-12-13T17:17:54Z |
| publishDate | 2011-11-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-5afaf0892fc44919816f3633d22880272022-12-21T23:37:23ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592011-11-017105Dolbeault Complex on S^4{·} and S^6{·} through Supersymmetric GlassesAndrei V. SmilgaS^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.http://dx.doi.org/10.3842/SIGMA.2011.105Dolbeaultsupersymmetry |
| spellingShingle | Andrei V. Smilga Dolbeault Complex on S^4{·} and S^6{·} through Supersymmetric Glasses Symmetry, Integrability and Geometry: Methods and Applications Dolbeault supersymmetry |
| title | Dolbeault Complex on S^4{·} and S^6{·} through Supersymmetric Glasses |
| title_full | Dolbeault Complex on S^4{·} and S^6{·} through Supersymmetric Glasses |
| title_fullStr | Dolbeault Complex on S^4{·} and S^6{·} through Supersymmetric Glasses |
| title_full_unstemmed | Dolbeault Complex on S^4{·} and S^6{·} through Supersymmetric Glasses |
| title_short | Dolbeault Complex on S^4{·} and S^6{·} through Supersymmetric Glasses |
| title_sort | dolbeault complex on s 4 · and s 6 · through supersymmetric glasses |
| topic | Dolbeault supersymmetry |
| url | http://dx.doi.org/10.3842/SIGMA.2011.105 |
| work_keys_str_mv | AT andreivsmilga dolbeaultcomplexons4ands6throughsupersymmetricglasses |