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Moduli Stabilising in Heterotic Nearly K\"ahler Compactifications
High Energy Physics - Theory · Submitted 22 Oct 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Our results show that heterotic nearly K\"ahler compactifications can lead to maximally symmetric four-dimensional space-times at the non-perturbative level.
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The abstract, sentence by sentence
We study heterotic string compactifications on nearly K\"ahler homogeneous spaces, including the gauge field effects which arise at order \alpha'. Using Abelian gauge fields, we are able to solve the Bianchi identity and supersymmetry conditions to this order. The four-dimensional external space-time consists of a domain wall solution with moduli fields varying along the transverse direction. We find that the inclusion of \alpha' corrections improves the moduli stabilization features of this solution. In this case, one of the dilaton and the volume modulus asymptotes to a constant value away from the domain wall. It is further shown that the inclusion of non-perturbative effects can stabilize the remaining modulus and "lift" the domain wall to an AdS vacuum. The coset SU(3)/U(1)^2 is used as an explicit example to demonstrate the validity of this AdS vacuum. Our results show that heterotic nearly K\"ahler compactifications can lead to maximally symmetric four-dimensional space-times at the non-perturbative level.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study heterotic string compactifications on nearly K\"ahler homogeneous spaces, including the gauge field effects which arise at order \alpha'. | contribution 0.99 | 0.92 | 0.04 | asserted 0.92 |
| s1 | Using Abelian gauge fields, we are able to solve the Bianchi identity and supersymmetry conditions to this order. | method 0.95 | 0.95 | 0.04 | asserted 0.99 |
| s2 | The four-dimensional external space-time consists of a domain wall solution with moduli fields varying along the transverse direction. | result 0.93 | 0.69 | 0.05 | asserted 1.00 |
| s3 | We find that the inclusion of \alpha' corrections improves the moduli stabilization features of this solution. | result 0.98 | 0.94 | 0.21 | asserted 1.00 |
| s4 | In this case, one of the dilaton and the volume modulus asymptotes to a constant value away from the domain wall. | result 1.00 | 0.85 | 0.06 | asserted 1.00 |
| s5 | It is further shown that the inclusion of non-perturbative effects can stabilize the remaining modulus and "lift" the domain wall to an AdS vacuum. | result 0.99 | 0.90 | 0.30 | asserted 1.00 |
| s6 | The coset SU(3)/U(1)^2 is used as an explicit example to demonstrate the validity of this AdS vacuum. | method 0.79 | 0.88 | 0.05 | asserted 1.00 |
| s7 | Our results show that heterotic nearly K\"ahler compactifications can lead to maximally symmetric four-dimensional space-times at the non-perturbative level. | result 0.56 | 0.91 | 0.84 | asserted 0.91 |
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Original abstract
We study heterotic string compactifications on nearly K\"ahler homogeneous spaces, including the gauge field effects which arise at order \alpha'. Using Abelian gauge fields, we are able to solve the Bianchi identity and supersymmetry conditions to this order. The four-dimensional external space-time consists of a domain wall solution with moduli fields varying along the transverse direction. We find that the inclusion of \alpha' corrections improves the moduli stabilization features of this solution. In this case, one of the dilaton and the volume modulus asymptotes to a constant value away from the domain wall. It is further shown that the inclusion of non-perturbative effects can stabilize the remaining modulus and "lift" the domain wall to an AdS vacuum. The coset SU(3)/U(1)^2 is used as an explicit example to demonstrate the validity of this AdS vacuum. Our results show that heterotic nearly K\"ahler compactifications can lead to maximally symmetric four-dimensional space-times at the non-perturbative level.
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References
How the literature uses it
20 arXiv papers cite this in 44 sentences
Papers citing it · 28 sentences without a confident label
Builds on it 2 papers
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Moreover, we consider previously unexplored combinations of instanton configurations thereby extending results of [ref] .
Order $\alpha'$ heterotic domain walls with warped nearly K\"ahler geometry · Introduction · 0.88
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A relatively straightforward study would be to extend the analysis of [ref] to the phase-changing flow of nearly Kähler manifolds that we discussed in section [ref].
Exploring SU(3) Structure Moduli Spaces with Integrable G2 Structures · Conclusions · 0.91
Compares with it 1 paper
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We see that in terms of the original variables $y$ and $h(y)$, this case is equivalent to the scenario discussed in [ref] , Section 4.5.2.
Order $\alpha'$ heterotic domain walls with warped nearly K\"ahler geometry · Explicit solutions with vanishing imaginary part of the first torsion class · 0.95
Cites it as background 9 papers
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More details and derivations can be found in Ref. [ref] and references therein.
Moduli in General $SU(3)$-Structure Heterotic Compactifications · The Coset $SU(3)/U(1)^2$ · 0.93
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It is known that effects at linear order in $α'$ can change the flow quite drastically for certain $SU(3)$ structure manifolds, see e.g. [ref] .
Exploring SU(3) Structure Moduli Spaces with Integrable G2 Structures · Conclusions · 0.82
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Significant progress has recently been made regarding the dimensional reduction of the $E_8×E_8$ Heterotic String using non-symmetric coset spaces [ref] - [ref] , in the presence of background fluxes and gaugino condensates.
Towards realistic models from Higher-Dimensional theories with Fuzzy extra dimensions · Introduction · 0.81
What it cites · 39 sentences without a confident label
Uses the method or tool of 5 papers
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The Kähler potential for the above set of fields is obtained from standard dimensional reduction [ref] as [equation] The superpotential is obtained from the generalized Gukov-Vafa-Witten formula [ref] [equation] After inserting the various forms from Eq. [ref] and [ref] and using Eq. [ref] as well as the properties of the half-flat mirror basis given in Section [ref] this leads to [equation] The first term arises from the non-vanishing torsion of the internal space and the second term is due to the non-vanishing H-flux induced by the gauge bundle.
Heterotic String Compactifications on Half-flat Manifolds II · Kähler potential and superpotential · 0.92
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The Kähler potential for the above set of fields is obtained from standard dimensional reduction [ref] as [equation] The superpotential is obtained from the generalized Gukov-Vafa-Witten formula [ref] [equation] After inserting the various forms from Eq. [ref] and [ref] and using Eq. [ref] as well as the properties of the half-flat mirror basis given in Section [ref] this leads to [equation] The first term arises from the non-vanishing torsion of the internal space and the second term is due to the non-vanishing H-flux induced by the gauge bundle.
Heterotic on Half-flat · Kähler potential and superpotential · 0.92
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The Kähler potential for the above set of fields is obtained from standard dimensional reduction [ref] as [equation] The superpotential is obtained from the generalized Gukov-Vafa-Witten formula [ref] [equation] After inserting the various forms from Eq. [ref] and [ref] and using Eq. [ref] as well as the properties of the half-flat mirror basis given in Section [ref] this leads to [equation] The first term arises from the non-vanishing torsion of the internal space and the second term is due to the non-vanishing H-flux induced by the gauge bundle.
CFT's From Calabi-Yau Four-folds · Kähler potential and superpotential · 0.92
Compares with 1 paper
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It follows that [equation] In fact, our proof holds for all domain wall compactifications on an internal manifold with $H^3(X)=0$ and, therefore, no nontrivial $H$-flux can be present in such geometries at lowest order[This result agrees with the findings of [ref] , which performed an extensive search for flux compactifications of the heterotic string on various known non-Calabi-Yau backgrounds including our cosets.].
Heterotic domain wall solutions and SU(3) structure manifolds · Bianchi identity · 0.83
Cites as support 1 paper
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However, for our cosets it has been shown [ref] that only torsion-free discrete groups can have a free action on $G/H$, that is, groups which do not posses any cyclic elements.
Compact Clifford-Klein forms of symmetric spaces -- revisited · Side issues: Kaluza-Klein gauge group and Wilson lines · 0.99
Cites as background 18 papers
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In this section we will review the solution at lowest order in $α'$ which has been found in Ref. [ref] .
Bundles over Nearly-Kahler Homogeneous Spaces in Heterotic String Theory · Solutions to lowest order in $α'$ · 0.86
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A more general class of heterotic non Calabi-Yau compactifications on half-flat mirror manifolds – manifolds which appear in the context of type II mirror symmetry with NS flux – has been introduced some time ago in Refs. [ref] .
Heterotic on Half-flat · Introduction · 0.97
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A more general class of heterotic non Calabi-Yau compactifications on half-flat mirror manifolds – manifolds which appear in the context of type II mirror symmetry with NS flux – has been introduced some time ago in Refs. [ref] .
G-structures and Domain Walls in Heterotic Theories · Introduction · 0.97
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