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: Jock McOrist, Martin Sticka, Eirik Eik Svanes
Format: Article
Language:English
Published: SpringerOpen 2025-05-01
Series:Journal of High Energy Physics
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Online Access:https://doi.org/10.1007/JHEP05(2025)219
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author Jock McOrist
Martin Sticka
Eirik Eik Svanes
author_facet Jock McOrist
Martin Sticka
Eirik Eik Svanes
author_sort Jock McOrist
collection DOAJ
description 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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spelling doaj-art-8a2228d3a3a045dc985bb23c9aa3ab442025-08-20T03:10:38ZengSpringerOpenJournal of High Energy Physics1029-84792025-05-012025513110.1007/JHEP05(2025)219The physical moduli of heterotic G 2 string compactificationsJock McOrist0Martin Sticka1Eirik Eik Svanes2Department of Mathematics, School of Science and Technology, University of New EnglandDepartment of Mathematics, School of Science and Technology, University of New EnglandDepartment of Mathematics and Physics, Faculty of Science and Technology, University of StavangerAbstract 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.https://doi.org/10.1007/JHEP05(2025)219Superstrings and Heterotic StringsSuperstring Vacua
spellingShingle Jock McOrist
Martin Sticka
Eirik Eik Svanes
The physical moduli of heterotic G 2 string compactifications
Journal of High Energy Physics
Superstrings and Heterotic Strings
Superstring Vacua
title The physical moduli of heterotic G 2 string compactifications
title_full The physical moduli of heterotic G 2 string compactifications
title_fullStr The physical moduli of heterotic G 2 string compactifications
title_full_unstemmed The physical moduli of heterotic G 2 string compactifications
title_short The physical moduli of heterotic G 2 string compactifications
title_sort physical moduli of heterotic g 2 string compactifications
topic Superstrings and Heterotic Strings
Superstring Vacua
url https://doi.org/10.1007/JHEP05(2025)219
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