Almost Calabi-Yau with torsion 6-manifolds and the instanton condition
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913935612968960 |
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| author | Ivanov, Stefan Ugarte, Luis |
| author_facet | Ivanov, Stefan Ugarte, Luis |
| contents | It is observed that on a compact almost complex Calabi-Yau with torsion (ACYT) 6-manifold with co-closed Lee form the curvature of the torsion connection is an $SU(3)$-instanton if and only if the torsion is parallel with respect to the torsion connection. The same conclusion holds for any (non necessarily compact) balanced ACYT 6-manifold. In particular, on a CYT 6-manifold the Strominger-Bismut connection is an $SU(3)$-instanton if and only if the torsion is parallel with respect to the Strominger-Bismut connection provided either the CYT 6-manifold is compact with co-closed Lee form or it is a balanced CYT 6-manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01655 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Almost Calabi-Yau with torsion 6-manifolds and the instanton condition Ivanov, Stefan Ugarte, Luis Differential Geometry High Energy Physics - Theory It is observed that on a compact almost complex Calabi-Yau with torsion (ACYT) 6-manifold with co-closed Lee form the curvature of the torsion connection is an $SU(3)$-instanton if and only if the torsion is parallel with respect to the torsion connection. The same conclusion holds for any (non necessarily compact) balanced ACYT 6-manifold. In particular, on a CYT 6-manifold the Strominger-Bismut connection is an $SU(3)$-instanton if and only if the torsion is parallel with respect to the Strominger-Bismut connection provided either the CYT 6-manifold is compact with co-closed Lee form or it is a balanced CYT 6-manifold. |
| title | Almost Calabi-Yau with torsion 6-manifolds and the instanton condition |
| topic | Differential Geometry High Energy Physics - Theory |
| url | https://arxiv.org/abs/2507.01655 |