REVIEW
Cosmological Implications of Dynamical Supersymmetry Breaking
High Energy Physics - Phenomenology · Submitted 18 Aug 1993 · 27 references
Pith's verdict: The taxonomy and the 3×10^4 GeV moduli bound are real and have held up, but the abstract's flat 'inflation cannot fix this' outruns the footnote it rests on, and 'all NRHS models' is overstated against the paper's own Section 2.4.
T0 · AI review
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Referee report
The paper
The paper claims
Models that break supersymmetry through Planck-suppressed operators leave behind light, gravitationally coupled scalars that wreck big bang nucleosynthesis, unless the gravitino mass exceeds about $3$ TeV.
The reading
What carries the argument
The load-bearing object is the set of singlet superfields $z_A$ in the hidden sector, together with the expansions of the Kähler potential and superpotential in powers of $z_A/M_P$ with coefficients of order one. Two conditions do the work: the vanishing-cosmological-constant constraint $F_A F_A = 3 |W|^2/M_P^2$, which ties the scale of R-symmetry breaking to the supersymmetry-breaking scale via $M_R^3 = M_S^2 M_P$, and the resulting mass estimate $m_{z} = M_R^3/M_P^2 = m_{3/2}$. From there the standard Polonyi-style cosmology — thermal misalignment, oscillation, gravitational decay, entropy dump — converts the mass estimate into a lower bound on the gravitino mass.
Extended reading notes
Core claim
The central claim is that the class the authors call NRHS — hidden-sector models whose supersymmetry breaking requires nonrenormalizable, Planck-suppressed operators — is cosmologically excluded. The argument is that such models contain gauge-singlet chiral superfields $z_A$ coupling to a strongly coupled sector only through terms like $c_A z_A O_4 / M_P$, so their masses come out of order $M_R^3/M_P^2$, i.e. of order the gravitino mass, with gravitational-strength couplings. Expanding the effective supergravity potential around the supersymmetry-breaking minimum, the authors show that the singlet masses are tied to the same coefficients that fix the cosmological constant and cannot be arbitrarily raised without making the dimensionless coefficients of the Kähler and superpotential expansions large — which, they argue, really signals new physics below the Planck scale and so means the model was never an NRHS model. A scalar of mass $m$ with gravitational couplings oscillates once $T < $ the appropriate scale, behaves as cold dark matter, and decays only after a time of order $M_P^2/m^3$, reheating the universe to at most $m^3/M_P$; requiring this to exceed $1$ MeV forces $m > 3$ GeV, far above the weak scale. Inflation does not help, because the condensate is regenerated. Hence NRHS models, including racetrack gaugino condensation and modulus-driven breaking, are ruled out in their natural form, and string theory must supply nonperturbative dynamics above about $10^{14}$ GeV that stabilizes moduli without breaking supersymmetry.
Load-bearing premise
The exclusion rests on the assumption that the dimensionless coefficients in the expansions of the Kähler potential and superpotential are of order one, so that the dangerous singlet masses really are of order the gravitino mass; the authors argue this by naturalness rather than by derivation, and concede that some coefficients could be much smaller than one.
Editorial extensions
If this is right
- All hidden-sector models whose breaking vanishes as $M_P \to \infty$ with an intermediate scale fixed — gaugino condensation, racetrack models, modulus F-term breaking — are excluded unless the gravitino mass exceeds roughly $3\times 10^4$ GeV.
- String theory must contain nonperturbative dynamics at or above $10^{14}$ GeV that fixes the moduli without breaking supersymmetry, so that moduli decay before nucleosynthesis.
- The viable options narrow to two: visible-sector dynamical breaking, where the breaking sector carries standard-model quantum numbers and communicates via gauge interactions, and hidden-sector models that break supersymmetry through renormalizable flat-space interactions.
- Hidden-sector flat-space breaking generically yields gauginos far lighter than squarks, so a light gluino or chargino is a signature of this class; visible-sector models instead give gauginos at the weak scale and automatically suppress flavor-changing neutral currents.
- In the flat-space hidden-sector models the R-axion can land in the invisible-axion window, so the same field that solves the strong CP problem may also set the gravitino mass at the weak scale.
Reading between the lines
- The bound can be read backwards as a constraint on reheating: any scenario that leaves the universe with a long-lived, gravitationally coupled scalar after inflation must reheat above roughly $m^3/M_P$, which ties early-universe thermal history to whatever stabilizes moduli.
- The argument is not specific to supersymmetry breaking — it applies to any light scalar whose only couplings are gravitational, so it also constrains light moduli, dilaton-like fields, and ultralight dark-energy candidates that were still rolling in the early universe.
- If the exclusion holds, the natural experimental target shifts: instead of searching for the heavy gravitino that NRHS models would require, one should look for the light gauginos and R-axion that the surviving flat-space models predict.
- The authors' own escape hatch — large dimensionless coefficients in the effective expansion — is testable in principle: a UV completion that produces such coefficients without new physics below $M_P$ would reopen the excluded class.
Original abstract
We provide a taxonomy of dynamical supersymmetry breaking theories, and discuss the cosmological implications of the various types of models. Models in which supersymmetry breaking is produced by chiral superfields which only have interactions of gravitational strength (\eg\ string theory moduli) are inconsistent with standard big bang nucleosynthesis unless the gravitino mass is greater than $\CO(3) \times 10^4$ GeV. This problem cannot be solved by inflation. Models in which supersymmetry is dynamically broken by renormalizable interactions in flat space have no such cosmological problems. Supersymmetry can be broken either in a hidden or the visible sector. However hidden sector models suffer from several naturalness problems and have difficulties in producing an acceptably large gluino mass.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
We provide a taxonomy of dynamical supersymmetry breaking theories, and discuss the cosmological implications of the various types of models. Models in which supersymmetry breaking is produced by chiral superfields which only have interactions of gravitational strength (\eg\ string theory moduli) are inconsistent with standard big bang nucleosynthesis unless the gravitino mass is greater than $\CO(3) \times 10^4$ GeV. This problem cannot be solved by inflation. Models in which supersymmetry is dynamically broken by renormalizable interactions in flat space have no such cosmological problems. Supersymmetry can be broken either in a hidden or the visible sector. However hidden sector models suffer from several naturalness problems and have difficulties in producing an acceptably large gluino mass.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We provide a taxonomy of dynamical supersymmetry breaking theories, and discuss the cosmological implications of the various types of models. | contribution 1.00 | 0.90 | 0.14 | asserted 0.92 |
| s1 | Models in which supersymmetry breaking is produced by chiral superfields which only have interactions of gravitational strength (\eg\ string theory moduli) are inconsistent with standard big bang nucleosynthesis unless the gravitino mass is greater than $\CO(3) \times 10^4$ GeV. | result 0.95 | 0.37 | 0.23 | asserted 1.00 |
| s2 | This problem cannot be solved by inflation. | result 0.80 | 0.51 | 0.11 | asserted 1.00 |
| s3 | Models in which supersymmetry is dynamically broken by renormalizable interactions in flat space have no such cosmological problems. | result 0.94 | 0.47 | 0.19 | asserted 1.00 |
| s4 | Supersymmetry can be broken either in a hidden or the visible sector. | background 0.99 | 0.09 | 0.04 | asserted 0.54 |
| s5 | However hidden sector models suffer from several naturalness problems and have difficulties in producing an acceptably large gluino mass. | background 0.45 | 0.20 | 0.07 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v1
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References
How the literature uses it
142 arXiv papers cite this in 174 sentences
Papers citing it · 117 sentences without a confident label
Cites it as support 2 papers
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Furthermore, scalars in the $100-1000$ TeV range are much more easily compatible with the absence of flavor changing neutral currents (FCNC), CP violation [ref] , and the cosmological moduli problems [ref] .
Unification and New Particles at the LHC · Introduction · 0.97
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Models of light scalar dark matter also prefer low inflation scale to suppress isocurvature perturbations [ref] .
New Ideas in Baryogenesis: A Snowmass White Paper · Contributor: Akshay Ghalsasi · 0.96
Cites it as background 52 papers
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One problem caused by such a singlet SUSY breaking field is so-called Polonyi problem [ref] and Polony-induced gravitino problem [ref] .
R-invariant New Inflation Model vs Supersymmetric Standard Model · Gravitino production in SUGRA model · 0.89
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It was noted long ago that these moduli could be displaced from their low-energy minima in the early universe, and their coherent oscillations lead to a period of matter domination [ref] .
Was the Universe Actually Radiation Dominated Prior to Nucleosynthesis? · Introduction · 0.81
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In particular, when the supergravity effect plays an essential role in supersymmetry breaking (termed the non-renormalizable hidden sector in Ref. [ref] ), the scalar superpartner of the goldstino often has interaction whose strength is similar to gravitational interaction, a mass, $m_ϕ$, of the order of the gravitino mass, $m_3/2$, and a vacuum expectation value of the Planck scale.
A Note on Polonyi Problem · Introduction · 0.84
Discussion
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