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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.16817 |
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Table of 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.