The physical moduli of heterotic G 2 string compactifications
Abstract In previous works, an operator was developed for heterotic compactifications on ℝ2,1 × G 2 and AdS 3 × 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 fre...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-05-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP05(2025)219 |
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| Summary: | Abstract In previous works, an operator was developed for heterotic compactifications on ℝ2,1 × G 2 and AdS 3 × 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 D ˇ $$ \overset{\check{} }{D} $$ that captures the physical moduli space of the G 2 heterotic string theory. When Y = X × S 1, with X an SU(3) manifold, we show D ˇ $$ \overset{\check{} }{D} $$ 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 D ˇ † $$ {\overset{\check{} }{D}}^{\dagger } $$ . We show the G 2 moduli correspond to the intersection of the kernels of D ˇ $$ \overset{\check{} }{D} $$ and D ˇ † $$ {\overset{\check{} }{D}}^{\dagger } $$ . These kernels reduce to the SU(3) F-terms and D-terms respectively on X × 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. |
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| ISSN: | 1029-8479 |