The physical moduli of heterotic G_2 string compactifications
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917930288021504 |
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| author | McOrist, Jock Sticka, Martin Svanes, Eirik Eik |
| author_facet | McOrist, Jock Sticka, Martin Svanes, Eirik Eik |
| contents | In previous works, an operator was developed for heterotic compactifications on $\mathbb{R}^{2,1}\times G_2$ and $AdS_3 \times G_2$, which preserves $N=1$ $d=3$ supersymmetry and whose kernel is related to the moduli of the compactification. The operator is described in terms of non-physical spurious degrees of freedom, specifically, deformations of a connection on the tangent bundle. In this paper, we eliminate these spurious degrees of freedom by linking deformations of the spin connection to the moduli of the $G_2$ manifold $Y$. This results in an operator $\check D$ that captures the physical moduli space of the $G_2$ heterotic string theory. When $Y=X\times S^1$, with $X$ an $SU(3)$ manifold, we show $\check D$ produces results that align with existing literature. This allows us to propose a $G_2$ moduli space metric. We check that this metric reduces to the $SU(3)$ moduli metric constructed in the literature. We then define an adjoint operator ${\check D}^†$. We show the $G_2$ moduli correspond to the intersection of the kernels of $\check D$ and ${\check D}^†$. These kernels reduce to the $SU(3)$ F-terms and D-terms respectively on $X\times S^1$. This gives two non-trivial consistency checks of our proposed moduli space metric. Working perturbatively in $α'$, we also demonstrate that the heterotic $G_2$ moduli problem can be characterised in terms of a double extension of ordinary bundles, just like in the $SU(3)$ case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_13080 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The physical moduli of heterotic G_2 string compactifications McOrist, Jock Sticka, Martin Svanes, Eirik Eik High Energy Physics - Theory In previous works, an operator was developed for heterotic compactifications on $\mathbb{R}^{2,1}\times G_2$ and $AdS_3 \times G_2$, which preserves $N=1$ $d=3$ supersymmetry and whose kernel is related to the moduli of the compactification. The operator is described in terms of non-physical spurious degrees of freedom, specifically, deformations of a connection on the tangent bundle. In this paper, we eliminate these spurious degrees of freedom by linking deformations of the spin connection to the moduli of the $G_2$ manifold $Y$. This results in an operator $\check D$ that captures the physical moduli space of the $G_2$ heterotic string theory. When $Y=X\times S^1$, with $X$ an $SU(3)$ manifold, we show $\check D$ produces results that align with existing literature. This allows us to propose a $G_2$ moduli space metric. We check that this metric reduces to the $SU(3)$ moduli metric constructed in the literature. We then define an adjoint operator ${\check D}^†$. We show the $G_2$ moduli correspond to the intersection of the kernels of $\check D$ and ${\check D}^†$. These kernels reduce to the $SU(3)$ F-terms and D-terms respectively on $X\times S^1$. This gives two non-trivial consistency checks of our proposed moduli space metric. Working perturbatively in $α'$, we also demonstrate that the heterotic $G_2$ moduli problem can be characterised in terms of a double extension of ordinary bundles, just like in the $SU(3)$ case. |
| title | The physical moduli of heterotic G_2 string compactifications |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2409.13080 |