The heterotic G$_2$-system on 2-step nilmanifolds endowed with principal torus bundles
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| Format: | Preprint |
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2025
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| _version_ | 1866915684885200896 |
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| author | Moroianu, Andrei Raffero, Alberto Vezzoni, Luigi |
| author_facet | Moroianu, Andrei Raffero, Alberto Vezzoni, Luigi |
| contents | We study the heterotic G$_2$-system on 7-dimensional 2-step nilmanifolds $M=Γ\backslash N$ endowed with principal torus bundles. We first prove that every invariant G$_2$-structure solving the system must be coclosed (under an additional calibration assumption when the dimension of the derived Lie algebra of $N$ is $3$). Then, we discuss the existence of solutions for all possible isomorphism classes of 7-dimensional 2-step nilpotent Lie algebras, and we provide examples with constant dilaton function both when the cosmological constant of the spacetime is zero and when it is nonzero. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_16817 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The heterotic G$_2$-system on 2-step nilmanifolds endowed with principal torus bundles Moroianu, Andrei Raffero, Alberto Vezzoni, Luigi Differential Geometry We study the heterotic G$_2$-system on 7-dimensional 2-step nilmanifolds $M=Γ\backslash N$ endowed with principal torus bundles. We first prove that every invariant G$_2$-structure solving the system must be coclosed (under an additional calibration assumption when the dimension of the derived Lie algebra of $N$ is $3$). Then, we discuss the existence of solutions for all possible isomorphism classes of 7-dimensional 2-step nilpotent Lie algebras, and we provide examples with constant dilaton function both when the cosmological constant of the spacetime is zero and when it is nonzero. |
| title | The heterotic G$_2$-system on 2-step nilmanifolds endowed with principal torus bundles |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2512.16817 |