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Tri-linear Couplings in an Heterotic Minimal Supersymmetric Standard Model
High Energy Physics - Theory · Submitted 10 Feb 2006
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We obtain non-zero Yukawa couplings for the three up-sector quarks, and vanishing R-parity violating terms.
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The abstract, sentence by sentence
We calculate, at the classical level, the superpotential tri-linear couplings of the only known globally consistent heterotic minimal supersymmetric Standard Model [ hep-th/0512149 ]. This recently constructed model is based on a compactification of the E_8 x E_8 heterotic string theory on a Calabi-Yau threefold with Z_2 fundamental group, coupled with a slope-stable holomorphic SU(5) vector bundle. In the observable sector the massless particle content is that of the three-family supersymmetric Standard Model with n=0,1,2 massless Higgs pairs, depending on the location in the vector bundle moduli space, and no exotic particles. We obtain non-zero Yukawa couplings for the three up-sector quarks, and vanishing R-parity violating terms. In particular, the proton is stable. Another interesting feature is the existence of tri-linear couplings, on the loci with massless Higgs pairs, generating \mu-mass parameters for the Higgs pairs and neutrino mass terms, with specific vector bundle moduli playing the role of right-handed neutrinos.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We calculate, at the classical level, the superpotential tri-linear couplings of the only known globally consistent heterotic minimal supersymmetric Standard Model [ hep-th/0512149 ]. | contribution 1.00 | 0.96 | 0.24 | asserted 1.00 |
| s1 | This recently constructed model is based on a compactification of the E_8 x E_8 heterotic string theory on a Calabi-Yau threefold with Z_2 fundamental group, coupled with a slope-stable holomorphic SU(5) vector bundle. | background 0.69 | 0.15 | 0.03 | asserted 1.00 |
| s2 | In the observable sector the massless particle content is that of the three-family supersymmetric Standard Model with n=0,1,2 massless Higgs pairs, depending on the location in the vector bundle moduli space, and no exotic particles. | result 0.46 | 0.46 | 0.07 | asserted 1.00 |
| s3 | We obtain non-zero Yukawa couplings for the three up-sector quarks, and vanishing R-parity violating terms. | result 1.00 | 0.95 | 0.25 | asserted 1.00 |
| s4 | In particular, the proton is stable. | interpretation 0.73 | 0.78 | 0.16 | asserted 1.00 |
| s5 | Another interesting feature is the existence of tri-linear couplings, on the loci with massless Higgs pairs, generating \mu-mass parameters for the Higgs pairs and neutrino mass terms, with specific vector bundle moduli playing the role of right-handed neutrinos. | result 0.82 | 0.89 | 0.17 | asserted 1.00 |
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The paper
Original abstract
We calculate, at the classical level, the superpotential tri-linear couplings of the only known globally consistent heterotic minimal supersymmetric Standard Model [ hep-th/0512149 ]. This recently constructed model is based on a compactification of the E_8 x E_8 heterotic string theory on a Calabi-Yau threefold with Z_2 fundamental group, coupled with a slope-stable holomorphic SU(5) vector bundle. In the observable sector the massless particle content is that of the three-family supersymmetric Standard Model with n=0,1,2 massless Higgs pairs, depending on the location in the vector bundle moduli space, and no exotic particles. We obtain non-zero Yukawa couplings for the three up-sector quarks, and vanishing R-parity violating terms. In particular, the proton is stable. Another interesting feature is the existence of tri-linear couplings, on the loci with massless Higgs pairs, generating \mu-mass parameters for the Higgs pairs and neutrino mass terms, with specific vector bundle moduli playing the role of right-handed neutrinos.
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References
How the literature uses it
27 arXiv papers cite this in 56 sentences
Papers citing it · 25 sentences without a confident label
Builds on it 1 paper
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Hence, all the results of [ref] carry over to these new constructions.
On heterotic model constraints · The infinite family · 0.80
Uses its data or values 1 paper
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It was also computed in [ref] that the spectrum contains $51$ vector bundle moduli, on top of the $11$ complex structure moduli and the $11$ Kähler moduli of the Calabi-Yau threefold $X$.
On heterotic model constraints · The heterotic standard model of CITEMARK48Z · 0.99
Compares with it 1 paper
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This should be compared to the similar situations seen in the vanishing of superpotential couplings [ref] which also arise from substructure of the geometric description of the vacuum in various forms.
Structure In The Heterotic Matter Field Kahler Potential · Conclusions · 1.00
Cites it as support 2 papers
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The surprise seen in string theory models (see [ref] for some examples) is that many of these couplings do vanish, even though there is no known associated symmetry that would account for such a feature.
Vanishing Yukawa Couplings and the Geometry of String Theory Models · Introduction · 0.96
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For instance, an heterotic vacuum on a smooth Calabi-Yau threefold $X$ with fundamental group $_1(X) = _2$ reproducing precisely the massless spectrum of the Minimal Supersymmetric Standard Model of particle physics has recently been found [ref] .
On a class of non-simply connected Calabi-Yau threefolds · Physics motivation · 0.99
Cites it as background 17 papers
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This is the Calabi-Yau threefold that was used in the heterotic standard model of [ref] , and was first constructed in [ref] .
On heterotic model constraints · The non-simply connected Calabi-Yau threefolds · 0.83
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In recent years, the focus has moved to a wider class of models based on general holomorphic vector bundles on the internal space which can lead to any of the three GUT groups mentioned above [ref] .
Exploring Positive Monad Bundles And A New Heterotic Standard Model · Introduction · 0.94
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It has long been known that, in the context of smooth Calabi-Yau compactifications of the heterotic string, superpotential couplings often vanish for no obvious four-dimensional reason [ref] (see [ref] for examples of some related work in an orbifold context).
Structure In The Heterotic Matter Field Kahler Potential · Introduction · 0.83
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