Local descriptions of the heterotic SU(3) moduli space
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916664318099456 |
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| author | de Lázari, Hannah Lotay, Jason D. Earp, Henrique Sá Svanes, Eirik Eik |
| author_facet | de Lázari, Hannah Lotay, Jason D. Earp, Henrique Sá Svanes, Eirik Eik |
| contents | The heterotic $SU(3)$ system, also known as the Hull--Strominger system, arises from compactifications of heterotic string theory to six dimensions. This paper investigates the local structure of the moduli space of solutions to this system on a compact 6-manifold $X$, using a vector bundle $Q=(T^{1,0}X)^* \oplus {End}(E) \oplus T^{1,0}X$, where $E\to X$ is the classical gauge bundle arising in the system. We establish that the moduli space has an expected dimension of zero. We achieve this by studying the deformation complex associated to a differential operator $\bar{D}$, which emulates a holomorphic structure on $Q$, and demonstrating an isomorphism between the two cohomology groups which govern the infinitesimal deformations and obstructions in the deformation theory for the system. We also provide a Dolbeault-type theorem linking these cohomology groups to Čech cohomology, a result which might be of independent interest, as well as potentially valuable for future research. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_04382 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local descriptions of the heterotic SU(3) moduli space de Lázari, Hannah Lotay, Jason D. Earp, Henrique Sá Svanes, Eirik Eik Differential Geometry High Energy Physics - Theory The heterotic $SU(3)$ system, also known as the Hull--Strominger system, arises from compactifications of heterotic string theory to six dimensions. This paper investigates the local structure of the moduli space of solutions to this system on a compact 6-manifold $X$, using a vector bundle $Q=(T^{1,0}X)^* \oplus {End}(E) \oplus T^{1,0}X$, where $E\to X$ is the classical gauge bundle arising in the system. We establish that the moduli space has an expected dimension of zero. We achieve this by studying the deformation complex associated to a differential operator $\bar{D}$, which emulates a holomorphic structure on $Q$, and demonstrating an isomorphism between the two cohomology groups which govern the infinitesimal deformations and obstructions in the deformation theory for the system. We also provide a Dolbeault-type theorem linking these cohomology groups to Čech cohomology, a result which might be of independent interest, as well as potentially valuable for future research. |
| title | Local descriptions of the heterotic SU(3) moduli space |
| topic | Differential Geometry High Energy Physics - Theory |
| url | https://arxiv.org/abs/2409.04382 |