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Explicit Soft Supersymmetry Breaking in the Heterotic M-Theory $B-L$ MSSM
High Energy Physics - Theory · Submitted 20 Dec 2020
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We then show that at a large number of points in K\"ahler moduli space that satisfy all "bundle" constraints, these coefficients are initial conditions for the renormalization group equations which, at low energy, lead to completely realistic physics satisfying all phenomenological constraints.
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The strongly coupled heterotic M-theory vacuum for both the observable and hidden sectors of the $B-L$ MSSM theory is reviewed, including a discussion of the "bundle" constraints that both the observable sector $SU(4)$ vector bundle and the a hidden sector bundle induced from a line bundle must satisfy. Gaugino condensation is then introduced within this context, and the hidden sector bundles that exhibit gaugino condensation are presented. The condensation scale is computed, singling out one line bundle whose associated condensation scale is low enough to be compatible with the energy scales available at the LHC. The corresponding region of K\"ahler moduli space where all bundle constraints are satisfied is presented. The generic form of the moduli dependent $F$-terms due to a gaugino superpotential - which spontaneously break $N=1$ supersymmetry in this sector - is presented and then given explicitly for the unique line bundle associated with the low condensation scale. The moduli dependent coefficients for each of the gaugino and scalar field soft supersymmetry breaking terms are computed leading to a low-energy effective Lagrangian for the observable sector matter fields. We then show that at a large number of points in K\"ahler moduli space that satisfy all "bundle" constraints, these coefficients are initial conditions for the renormalization group equations which, at low energy, lead to completely realistic physics satisfying all phenomenological constraints. Finally, we show that a substantial number of these initial points also satisfy a final constraint arising from the quadratic Higgs-Higgs conjugate soft supersymmetry breaking term.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The strongly coupled heterotic M-theory vacuum for both the observable and hidden sectors of the $B-L$ MSSM theory is reviewed, including a discussion of the "bundle" constraints that both the observable sector $SU(4)$ vector bundle and the a hidden sector bundle induced from a line bundle must satisfy. | background 0.79 | 0.34 | 0.03 | asserted 0.91 |
| s1 | Gaugino condensation is then introduced within this context, and the hidden sector bundles that exhibit gaugino condensation are presented. | contribution 0.72 | 0.68 | 0.03 | asserted 0.98 |
| s2 | The condensation scale is computed, singling out one line bundle whose associated condensation scale is low enough to be compatible with the energy scales available at the LHC. | result 0.95 | 0.90 | 0.08 | asserted 0.99 |
| s3 | The corresponding region of K\"ahler moduli space where all bundle constraints are satisfied is presented. | result 0.74 | 0.86 | 0.04 | asserted 0.98 |
| s4 | The generic form of the moduli dependent $F$-terms due to a gaugino superpotential - which spontaneously break $N=1$ supersymmetry in this sector - is presented and then given explicitly for the unique line bundle associated with the low condensation scale. | contribution 0.63 | 0.88 | 0.06 | asserted 1.00 |
| s5 | The moduli dependent coefficients for each of the gaugino and scalar field soft supersymmetry breaking terms are computed leading to a low-energy effective Lagrangian for the observable sector matter fields. | contribution 0.52 | 0.93 | 0.08 | asserted 1.00 |
| s6 | We then show that at a large number of points in K\"ahler moduli space that satisfy all "bundle" constraints, these coefficients are initial conditions for the renormalization group equations which, at low energy, lead to completely realistic physics satisfying all phenomenological constraints. | result 0.95 | 0.93 | 0.68 | asserted 1.00 |
| s7 | Finally, we show that a substantial number of these initial points also satisfy a final constraint arising from the quadratic Higgs-Higgs conjugate soft supersymmetry breaking term. | result 0.97 | 0.94 | 0.24 | asserted 1.00 |
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Original abstract
The strongly coupled heterotic M-theory vacuum for both the observable and hidden sectors of the $B-L$ MSSM theory is reviewed, including a discussion of the "bundle" constraints that both the observable sector $SU(4)$ vector bundle and the a hidden sector bundle induced from a line bundle must satisfy. Gaugino condensation is then introduced within this context, and the hidden sector bundles that exhibit gaugino condensation are presented. The condensation scale is computed, singling out one line bundle whose associated condensation scale is low enough to be compatible with the energy scales available at the LHC. The corresponding region of K\"ahler moduli space where all bundle constraints are satisfied is presented. The generic form of the moduli dependent $F$-terms due to a gaugino superpotential - which spontaneously break $N=1$ supersymmetry in this sector - is presented and then given explicitly for the unique line bundle associated with the low condensation scale. The moduli dependent coefficients for each of the gaugino and scalar field soft supersymmetry breaking terms are computed leading to a low-energy effective Lagrangian for the observable sector matter fields. We then show that at a large number of points in K\"ahler moduli space that satisfy all "bundle" constraints, these coefficients are initial conditions for the renormalization group equations which, at low energy, lead to completely realistic physics satisfying all phenomenological constraints. Finally, we show that a substantial number of these initial points also satisfy a final constraint arising from the quadratic Higgs-Higgs conjugate soft supersymmetry breaking term.
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References
How the literature uses it
7 arXiv papers cite this in 21 sentences
Papers citing it · 13 sentences without a confident label
Builds on it 1 paper
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Building on this work, in Section 2.6, which follows [ref] , we attach a possible SUSY-breaking mechanism, namely gaugino condensation in the hidden sector.
The strongly coupled $E_8\times E_8$ heterotic string: Geometry $\&$ Phenomenology · Outline · 1.00
Uses its method or tool 1 paper
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In [ref] , as used in the discussion thus far in this paper, it was most convenient to solve all the mathematical and physical constraints by using the scaling in [ref] to choose a specific moduli gauge, called “unity gauge”, defined by
Stable Vacua with Realistic Phenomenology and Cosmology in Heterotic M-theory Satisfying Swampland Conjectures · Enhancing the range of Pfaffian parameter $p$: · 0.95
Uses its data or values 3 papers
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They were given in [ref] , for example.
Hidden Sectors from Multiple Line Bundles for the $B-L$ MSSM · Anomaly Cancellation · 0.99
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where $η̃= η/M_P$ and $ϕ̃= ϕ/M_P$, $M_P=1.22 ×10^19$ GeV is the four dimensional Planck mass, and the unification scale is canonically fixed to $M_U =3.15 ×10^16$ GeV [ref] .
Stable Vacua with Realistic Phenomenology and Cosmology in Heterotic M-theory Satisfying Swampland Conjectures · Deriving the potential energy · 0.86
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For example, in [ref] , the non-Abelian group is $E_7$ with the renormalization group coefficient
Moduli Axions, Stabilizing Moduli and the Large Field Swampland Conjecture in Heterotic M-Theory · Gaugino Condensate Superpotential · 0.96
Cites it as background 2 papers
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Hidden sectors with anomalous $U(1)$ factors have been studied in [ref] .
FIMP Dark Matter in Heterotic M-Theory · Moduli Mass Eigenstates–Anomalous U(1) Case · 0.97
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This configuration has been analyzed in a number of papers [ref] .
Moduli and Hidden Matter in Heterotic M-Theory with an Anomalous $U(1)$ Hidden Sector · Vanishing FI Term · 0.96
What it cites · 159 sentences without a confident label
Uses the method or tool of 2 papers
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In Section 5, using the formalism presented in [ref] and the results of Section 4, we compute the moduli dependent coefficients of the soft supersymmetry breaking terms of the matter fields in the $B-L$ MSSM observable sector.
Model-Independent Analysis of Soft Terms in Effective Supergravity and in String Theory · Introduction · 1.00
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To align with the formalism presented in [ref] and [ref] , where the general form of the soft supersymmetry breaking terms in the Lagrangian which we use in this analysis were computed, we rewrite the superpotential [ref] in the form
Five--Branes and Supersymmetry Breaking in M--Theory · Soft Supersymmetry Breaking Terms in the Observable Sector · 0.94
Uses data or values from 2 papers
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As discussed in [ref] and Section 2, we find that $⟨α_u⟩=1/20.08$ in the split Wilson lines scenario and $⟨α_u⟩=1/26.64$ in the simultaneous Wilson lines scenario (with $α=g^(1)2/4π$).
Line Bundle Hidden Sectors for Strongly Coupled Heterotic Standard Models · Gaugino Condensation · 0.94
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The upper and lower bounds for $tanβ$ are taken from [ref] and are consistent with present bounds that ensure perturbative Yukawa couplings.
A Supersymmetry Primer · Realistic Soft Supersymmetry Breaking Terms · 0.86
Compares with 5 papers
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This should be compared with previous work [ref] where, having no theory for calculating any of the soft supersymmetry breaking terms (the gauginos, cubic scalars and scalar mass terms) one was forced to chose the values of each of these 24 independent coefficients statistically.
$R$-parity Violating Decays of Wino Chargino and Wino Neutralino LSPs and NLSPs at the LHC · Realistic Soft Supersymmetry Breaking Terms · 1.00
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This should be compared with previous work [ref] where, having no theory for calculating any of the soft supersymmetry breaking terms (the gauginos, cubic scalars and scalar mass terms) one was forced to chose the values of each of these 24 independent coefficients statistically.
A Statistical Analysis of the Minimal SUSY B-L Theory · Realistic Soft Supersymmetry Breaking Terms · 1.00
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This should be compared with previous work [ref] where, having no theory for calculating any of the soft supersymmetry breaking terms (the gauginos, cubic scalars and scalar mass terms) one was forced to chose the values of each of these 24 independent coefficients statistically.
Supersymmetric Sneutrino-Higgs Inflation · Realistic Soft Supersymmetry Breaking Terms · 1.00
Cites as support 1 paper
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As proven in detail in [ref] , the $SU(4)$ vector bundle is slope-stable, and hence, satisfies the Hermitian Yang–Mills equations [ref] , in a restricted region of the positive Kähler cone specified by
Stability of the Minimal Heterotic Standard Model Bundle · Observable Sector Constraints · 0.96
Cites as background 23 papers
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In Section 2, we briefly review both the observable and hidden sectors of the heterotic M-theory $B-L$ MSSM vacuum presented in [ref] .
Line Bundle Hidden Sectors for Strongly Coupled Heterotic Standard Models · Introduction · 0.87
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This theory was further compactified to five-dimensional “heterotic” M-theory on a Calabi–Yau threefold in [ref] and then, by integrating out the $S^1/ℤ_2$ modes, to a four-dimensional effective $E_8 ×E_8$ heterotic string theory [ref] .
Heterotic M-theory in Five Dimensions · Introduction · 0.95
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This theory was further compactified to five-dimensional “heterotic” M-theory on a Calabi–Yau threefold in [ref] and then, by integrating out the $S^1/ℤ_2$ modes, to a four-dimensional effective $E_8 ×E_8$ heterotic string theory [ref] .
The Universe as a Domain Wall · Introduction · 0.95
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