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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.14715 |
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| _version_ | 1866914160648912896 |
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| author | de la Ossa, Xenia Larfors, Magdalena Magill, Matthew Svanes, Eirik E. |
| author_facet | de la Ossa, Xenia Larfors, Magdalena Magill, Matthew Svanes, Eirik E. |
| contents | Compactifications of the heterotic string, to first order in the $α'$ expansion, on manifolds with integrable $G_2$ structure give rise to three-dimensional ${\cal N} = 1$ supergravity theories that admit Minkowski and AdS ground states. As shown in arXiv:1904.01027, such vacua correspond to critical loci of a real superpotential $W$. We perform a perturbative study around a supersymmetric vacuum of the theory, which confirms that the first order variation of the superpotential, $δW$, reproduces the BPS conditions for the system, and furthermore shows that $δ^2 W=0$ gives the equations for infinitesimal moduli. This allows us to identify a nilpotent differential, and a symplectic pairing, which we use to construct a bicomplex, or a double complex, for the heterotic $G_2$ system. Using this complex, we determine infinitesimal moduli and their obstructions in terms of related cohomology groups. Finally, by interpreting $δ^2 W$ as an action, we compute the one-loop partition function of the heterotic $G_2$ system and show it can be decomposed into a product of one-loop partition functions of Abelian and non-Abelian instanton gauge theories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_14715 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum aspects of heterotic $G_2$ systems de la Ossa, Xenia Larfors, Magdalena Magill, Matthew Svanes, Eirik E. High Energy Physics - Theory Compactifications of the heterotic string, to first order in the $α'$ expansion, on manifolds with integrable $G_2$ structure give rise to three-dimensional ${\cal N} = 1$ supergravity theories that admit Minkowski and AdS ground states. As shown in arXiv:1904.01027, such vacua correspond to critical loci of a real superpotential $W$. We perform a perturbative study around a supersymmetric vacuum of the theory, which confirms that the first order variation of the superpotential, $δW$, reproduces the BPS conditions for the system, and furthermore shows that $δ^2 W=0$ gives the equations for infinitesimal moduli. This allows us to identify a nilpotent differential, and a symplectic pairing, which we use to construct a bicomplex, or a double complex, for the heterotic $G_2$ system. Using this complex, we determine infinitesimal moduli and their obstructions in terms of related cohomology groups. Finally, by interpreting $δ^2 W$ as an action, we compute the one-loop partition function of the heterotic $G_2$ system and show it can be decomposed into a product of one-loop partition functions of Abelian and non-Abelian instanton gauge theories. |
| title | Quantum aspects of heterotic $G_2$ systems |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2412.14715 |