Recent Developments in Heterotic Moduli
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910627478372352 |
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| author | Ibarra, Javier José Murgas Svanes, Eirik Eik |
| author_facet | Ibarra, Javier José Murgas Svanes, Eirik Eik |
| contents | We review recent results for heterotic moduli and the Hull--Strominger system. In particular, we discuss mathematical properties of the recently derived deformation operator $\bar D$ associated to the deformation complex of heterotic $SU(3)$ solutions. We review results on Serre duality, showing that the operator has a vanishing index, and discuss a notion of Čech cohomology and a particular instance of a Dolbeault theorem for $\bar D$. Specifically, the cohomology parametrising infinitesimal deformations is isomorphic to the first Čech cohomology of an associated cochain complex. This will be useful for future research, as it provides a more algebraic handle on the heterotic moduli problem, which is useful for understanding notions of stability, geometric invariants, and enumerative geometry for the Hull--Strominger system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_16524 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Recent Developments in Heterotic Moduli Ibarra, Javier José Murgas Svanes, Eirik Eik High Energy Physics - Theory We review recent results for heterotic moduli and the Hull--Strominger system. In particular, we discuss mathematical properties of the recently derived deformation operator $\bar D$ associated to the deformation complex of heterotic $SU(3)$ solutions. We review results on Serre duality, showing that the operator has a vanishing index, and discuss a notion of Čech cohomology and a particular instance of a Dolbeault theorem for $\bar D$. Specifically, the cohomology parametrising infinitesimal deformations is isomorphic to the first Čech cohomology of an associated cochain complex. This will be useful for future research, as it provides a more algebraic handle on the heterotic moduli problem, which is useful for understanding notions of stability, geometric invariants, and enumerative geometry for the Hull--Strominger system. |
| title | Recent Developments in Heterotic Moduli |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2409.16524 |