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Matter symmetries in supersymmetric standard models from non-invertible selection rules

T0 review · 2 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper shows that a remnant Z2 symmetry of the Ising fusion algebra acts as R-parity in the supersymmetric standard model, forbidding baryon- and lepton-number-violating operators, and that the same non-invertible selection rules can…

desk verdict Solid classification of MSSM matter symmetries from Z2-gauged fusion rules; the Weinberg-operator no-go is a real result, but the all-loop R-parity claim is asserted, not proven. read the letter →

arxiv 2506.10241 v1 pith:LZBQXLGO submitted 2025-06-11 hep-ph hep-th

Tatsuo Kobayashi , Hironobu Mita , Hajime Otsuka , Riku Sakuma This is my paper
classification hep-phhep-th
keywords non-invertiblesymmetriesselectionrulesR-paritysupersymmetricstandardmodelbaryontrialityprotonhexalityIsingfusionrulemagnetizedorbifoldcompactification
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper asks whether the coupling selection rules of a supersymmetric standard model can come from non-invertible symmetries rather than from a conventional discrete gauge group. It works out, field by field, the possible assignments of the seven chiral superfields to classes of the fusion algebras obtained by Z2-gauging Z3, Z4, and Z5, keeping only assignments that allow the three Yukawa couplings. The central result is that in the Z4 (Ising) case a leftover Z2 grading of the fusion algebra behaves exactly like R-parity, forbidding the baryon- and lepton-number-violating operators that would otherwise cause fast proton decay. The same selection rules, combined with the Standard Model gauge symmetry, can realize baryon triality and proton hexality, and the Weinberg operator LHuLHu is always allowed. A sympathetic reader would take the paper as showing that non-invertible selection rules could supply the proton-stability and dark-matter-stability matter symmetries from the underlying geometry, rather than by flat.

What carries the argument

The machinery is Z2-gauging of a ZM symmetry: start with a ZM group generated by g, and orbifold by the outer automorphism r: g ↦ g−1; a field organizes into a class [g^k] = {g^k, $g^{{M−k}}$} and behaves as if it carried both charges k and M−k simultaneously. The classes obey the fusion rule [g^k][$g^{{k'}}$] = [$g^{{k+k'}}$] + [$g^{{M−k−k'}}$], which for M=3 gives the Fibonacci fusion rule and for M=4 gives the Ising fusion rule. An n-point coupling of fields with classes [$g^{{k_i}}$] is allowed exactly when the identity class [$g^{0}$] appears in the fusion product, equivalently ∑ ±k_i ≡ 0 (mod M). For even M this algebra carries an automatic Z2 grading (even versus odd k), and it is this grading, present in the Ising fusion rule, that the paper identifies with R-parity; the tables of all consistent assignments are the working tool that maps each fusion pattern to its allowed operators.

What would settle it

A direct string or field-theory calculation that exhibits a non-zero amplitude for a process with an odd number of Z2-odd ([g1]) external states, for example the operator LHu in the M=4 assignment (32), at any loop order would disprove the all-loop exactness of the Z2 grading and with it the R-parity claim. Equivalently, constructing the magnetized orbifold model for a GUT-consistent assignment and finding that radiative corrections generate any coupling the fusion rules forbid at tree level would falsify the paper's central conclusion.

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Extended reading notes

Core claim

The paper's claim is that family-independent assignments of MSSM chiral superfields to the classes of Z2-gauged ZM fusion algebras give rise to the same coupling selection rules as the well-known discrete matter symmetries R-parity (R2), baryon triality (B3), and proton hexality (P6), without any of these ZN symmetries being imposed. In the Ising fusion case (M=4), the class [g1] carries a Z2 charge while [g0] and [g2] are even; whenever Hu and Hd sit in even classes and the five matter superfields sit in the odd class, all dimension-4 baryon- and lepton-number-violating operators and most dimension-5 operators are forbidden, which is exactly R-parity. The paper further claims that this Z2 grading is a property of the fusion algebra itself and therefore survives at all-loop order, in contrast to the selection-rule constraints that radiative corrections generally break. It also claims that no assignment of these fusion classes can forbid the Weinberg operator LHuLHu, so the non-invertible selection rules cannot reproduce every conventional ZN matter symmetry.

Load-bearing premise

The argument assumes that a consistent ultraviolet completion (such as a magnetized orbifold compactification) exists in which the MSSM spectrum carries these fusion-class assignments, and that the Z2 grading of the Ising fusion algebra is an exact symmetry of the full quantum effective action to all loop orders.

Editorial extensions

If this is right

  • If the central claim is correct, the lightest supersymmetric particle is automatically stable as a dark-matter candidate in the R-parity-realizing assignments, with no R-parity imposed by hand.
  • Proton decay through dimension-4 and most dimension-5 operators is forbidden by the fusion selection rules, so the fast proton decay problem of the MSSM could be solved from the underlying symmetry structure.
  • Baryon triality and proton hexality can emerge as effective symmetries from the combination of the Standard Model gauge symmetry with the fusion rules, even though no Z3 or Z6 symmetry is imposed.
  • The Weinberg operator LHuLHu is always allowed, so the non-invertible selection rules are compatible with Majorana neutrino masses while still protecting the proton, a combination that some conventional ZN symmetries cannot achieve.
  • Some of the consistent assignments are compatible with SU(5), Pati-Salam, and SO(10) grand unified theories, so the mechanism can sit inside a grand unified framework.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the all-loop claim survives scrutiny, it would give a geometric or dynamical origin for R-parity in string-derived models, possibly explaining why R-parity is exact even though other fusion selection rules are radiatively broken; the paper asserts the all-loop property but does not derive it, so the special status of the Z2 grading within the fusion category needs a proof.
  • The systematic enumeration for M=3, 4, and 5 suggests that larger M or other fusion categories could realize the Weinberg-operator-forbidding ZN symmetries (such as R3 or L3) that this paper finds impossible, and that question is directly testable.
  • A concrete next step would be to construct an explicit magnetized orbifold model realizing one of the GUT-consistent assignments, for example the M=4 case (32), and check at one loop whether the Z2 grading is indeed preserved; the geometric realization is assumed rather than demonstrated.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The paper studies family-independent coupling selection rules in the MSSM that arise from Z2-gauged ZM symmetries, whose fusion algebras are the Fibonacci rule for M=3, the Ising rule for M=4, and the M=5 case. For each M, it enumerates all assignments of the seven chiral superfields Q, Hu, Hd, Ubar, Dbar, Ebar, L to fusion classes that allow the MSSM Yukawa couplings, and tabulates which dimension-4 and dimension-5 operators are allowed in F- and D-terms. It then identifies assignments whose allowed operators match the conventional discrete symmetries R2, B3, and P6, and claims that in the Ising case a remnant Z2 grading provides R-parity that is exact at all loop orders. It also marks which assignments are compatible with SU(5), Pati-Salam, and SO(10) GUT representations.

Significance. The paper's main value is as a systematic catalog: the assignment tables and operator lists are explicit, easily reproducible, and directly useful for model building, and the observation that the Weinberg operator is always allowed is a clean, non-trivial algebraic consequence of the fusion rules. If the all-loop exactness claim were proven, the result would give a UV-motivated origin of R-parity from non-invertible symmetry, which would be significant for dark matter and proton stability in string-derived models. As it stands, however, the headline conclusion is not established; the paper's own caveat about radiative corrections and the absence of any derivation of all-loop protection mean the statement has the status of a conjecture. The GUT-consistency columns are a useful addition, provided the embedding rule is documented.

major comments (2)
  1. [§4, Eq. (4.2); Abstract; Conclusions] The central claim that the Z2 grading of the Ising fusion rule (4.2) is an exact all-loop symmetry is asserted without derivation. The grading [g1] to -[g1] is a property of the fusion ring, i.e., a statement about which tree-level products contain [g0]; by itself it does not imply a symmetry of the quantum effective action. The Introduction itself states that radiative corrections will break non-invertible selection rules in general, and the paper provides no argument (e.g., a topological defect or discrete gauge symmetry surviving in the magnetized orbifold realizations of Refs. [16, 17]) that this particular Z2 is protected while the rest of the selection rules are not. Because the R-parity and LSP-stability conclusions rest on this point, the authors should either supply a derivation or explicitly state in the abstract and conclusions that the all-loop exactness is a conjecture.
  2. [§4, Tables 10 and 11] The identification of the assignments in Tables 10 and 11 with R2, B3, and P6 is made by comparing the sets of allowed operators in Tables 8-9 with the Z_N results in Tables 2-3. Matching a finite list of allowed operators does not demonstrate that the effective action possesses the corresponding Z_N symmetry; non-invertible selection rules could coincide with a Z2 symmetry on these operators but differ on other couplings. Unless a proof of the equivalence is given, the paper should state that the match is at the level of the listed operators only.
minor comments (5)
  1. [Abstract] The phrase 'In general, our finding selection rules can not realize the same results as conventional Z_N symmetries' is vague and ungrammatical; the precise statement in Section 4 is that the Weinberg operator is always allowed, unlike the Z_N symmetries that forbid it, and the abstract should be rephrased accordingly.
  2. [Table 7 caption] The caption states that the symbol ✓ or ∗ is introduced if the Z2 symmetry exists, but the table uses ✓ and ∗ for two different notions (remnant Z4 versus Ising-derived Z2); the distinction should be explained directly in the caption rather than only in the main text.
  3. [§4, paragraph after Table 7] There is a typo 'N = 4' in the paragraph following Table 7; it should read 'M = 4' to match the notation used in the rest of the paper.
  4. [§4, Tables 4-14] The GUT consistency columns are never defined: the authors should state the embedding rule (e.g., fields in the same GUT multiplet must share the same fusion class) and illustrate it on at least one representative assignment.
  5. [Tables 8 and 9] Several rows group many assignments together (e.g., '(16), (18), (21)'), which makes verification cumbersome; consider listing each assignment separately or adding a compact grid with per-case check marks.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the fusion-algebra rules are applied as external inputs, and the R-parity correspondence is read off enumerated charge assignments rather than fitted or defined into the result.

full rationale

The paper's derivation chain is a model-building enumeration, not a fit. The selection rule (2.11) with the sign condition on classes follows from the fusion product (2.6), and the Ising rule (4.2) is then applied to assign MSSM fields; Tables 4 and 7 list all assignments consistent with the Yukawa couplings, so the Z2 charges that reproduce R2, B3, and P6 are found by exhaustive search rather than by defining the target symmetry into the input. The statement that the Weinberg operator LHuLHu is always allowed is a genuine algebraic consequence of [gk][gk] always containing [g0], and the negative result that the Weinberg-forbidding Z_N symmetries cannot be reproduced is a non-trivial distinction from the conventional classification of Ref. [33]. Self-citations to Refs. [16,17,22] supply the framework and the compactification realization, but the applied rule is restated in Section 2 and is not a load-bearing argument that reduces to an unverified self-citation. The one caveat is that the claim that the remnant Z2 symmetry 'holds at all-loop order' (Abstract; Section 5) is asserted without derivation and sits in tension with the Introduction's remark that radiative corrections generally break non-invertible selection rules; that is an unsupported premise and a correctness risk, but it is not a circular step because the Z2 grading is not defined in terms of R-parity and no fitted parameter is renamed as a prediction. Score 0 for circularity.

Assumptions & free parameters 1 free parameters · 3 assumptions · 0 invented entities

No continuous free parameters are fitted. The class assignments are discrete choices whose values matter for the R-parity, baryon triality, and proton hexality outcomes. The main unproved input is the all-loop exactness of the Z2 grading.

free parameters (1)
  • Fusion class assignment (k_Q, k_Hu, k_Hd, k_U, k_D, k_E, k_L) = 0, 1, or 2 depending on M and case; e.g., (1,0,0,1,1,1,1) for M=4 case (32)
    The central results depend on which class each MSSM field is assigned. The paper enumerates all assignments preserving Yukawa terms, and the specific R-parity cases are (32), (43), (74), (85) for M=4.
assumptions (3)
  • domain assumption The coupling selection rule of Eq. (2.11), sum of signed class labels vanishes mod M, is the correct low-energy selection rule for all n-point couplings.
    Taken from prior work on Z2-gauged ZM symmetries in magnetized orbifold models [16]; the paper applies it to MSSM matter without re-deriving it.
  • domain assumption Each MSSM superfield corresponds to a single class [g_k], and fields in the same GUT multiplet must share the same class for GUT consistency.
    Used in Section 4 and Tables 4, 7, 12 to mark SU(5), Pati-Salam, and SO(10) compatibility; no derivation of why the orbifold projection preserves this assignment.
  • ad hoc to paper The Z2 grading of the Ising fusion rule (g1 odd, g0/g2 even) is an exact symmetry at all loop orders.
    Stated in the abstract and Conclusions without proof; the Introduction notes radiative corrections generally break non-invertible selection rules, so this assumption is introduced specifically to support the R-parity stability claim.

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Pith. "Pith review of Matter symmetries in supersymmetric standard models from non-invertible selection rules." pith.science (2026). https://pith.science/paper/LZBQXLGO

@misc{pith2026250610241,
  author       = {Pith},
  title        = {Pith review of: Matter symmetries in supersymmetric standard models from non-invertible selection rules},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LZBQXLGO}},
  note         = {Machine review of arXiv:2506.10241}
}
abstract

We discuss phenomenological implications of non-invertible selection rules in the framework of the supersymmetric standard model. We find that a remnant $\mathbb{Z}_2$ symmetry of fusion algebras which holds at all-loop order plays the role of $R$-parity, forbidding baryon and lepton violating operators. In addition, a combination of Standard Model gauge symmetry and the non-invertible selection rules lead to baryon triality and proton hexality that can protect the proton from decay. In general, our finding selection rules can not realize the same results as conventional $\mathbb{Z}_N$ symmetries in the supersymmetric standard model. We also clarify the assignments of matter fields under the fusion algebras that are consistent with $SU(4) \times SU(2) \times SU(2)$, $SU(5)$, and $SO(10)$ grand unified theories.

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Forward citations

Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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    Electron and muon masses are generated at one loop through loop-level breaking of the Ising fusion rule, while neutrino masses arise from an unbroken Z2-like sector that stabilizes loop particles.

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Reference graph

Works this paper leans on

39 extracted references · 4 canonical work pages · cited by 6 Pith papers

  1. [1]

    Schafer-Nameki, ICTP lectures on (non-)invertible generalized symmetries, Phys

    S. Schafer-Nameki, ICTP lectures on (non-)invertible generalized symmetries, Phys. Rept. 1063 (2024) 1 [ 2305.18296]

    arXiv 2024

  2. [2]

    Shao, What’s Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries, 2308.00747

    S.-H. Shao, What’s Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries, 2308.00747

    arXiv

  3. [3]

    Bhardwaj and Y

    L. Bhardwaj and Y. Tachikawa, On finite symmetries and their gauging in two dimensions, JHEP 03 (2018) 189 [ 1704.02330]

    arXiv 2018

  4. [4]

    Chang, Y.-H

    C.-M. Chang, Y.-H. Lin, S.-H. Shao, Y. Wang and X. Yin, Topological Defect Lines and Renormalization Group Flows in Two Dimensions, JHEP 01 (2019) 026 [ 1802.04445]

    arXiv 2019

  5. [5]

    Heidenreich, J

    B. Heidenreich, J. McNamara, M. Montero, M. Reece, T. Rudelius and I. Valenzuela, Non-invertible global symmetries and completeness of the spectrum, JHEP 09 (2021) 203 [2104.07036]

    arXiv 2021

  6. [6]

    Kaidi, K

    J. Kaidi, K. Ohmori and Y. Zheng, Kramers-Wannier-like Duality Defects in (3+1)D Gauge Theories, Phys. Rev. Lett.128 (2022) 111601 [ 2111.01141]

    arXiv 2022

  7. [7]

    Y. Choi, C. Cordova, P.-S. Hsin, H.T. Lam and S.-H. Shao, Noninvertible duality defects in 3+1 dimensions, Phys. Rev. D105 (2022) 125016 [ 2111.01139]

    arXiv 2022

  8. [8]

    J. Dong, T. Kobayashi, R. Nishida, S. Nishimura and H. Otsuka, Coupling Selection Rules in Heterotic Calabi-Yau Compactifications, 2504.09773

    arXiv

Show all 39 references
  1. [9]

    Dijkgraaf, E.P

    R. Dijkgraaf, E.P. Verlinde and H.L. Verlinde, C = 1 Conformal Field Theories on Riemann Surfaces, Commun. Math. Phys.115 (1988) 649

    1988

  2. [10]

    Kobayashi, S

    T. Kobayashi, S. Raby and R.-J. Zhang, Searching for realistic 4d string models with a Pati-Salam symmetry: Orbifold grand unified theories from heterotic string compactification on a Z(6) orbifold, Nucl. Phys. B 704 (2005) 3 [ hep-ph/0409098]

    2005 arXiv

  3. [11]

    Kobayashi, H.P

    T. Kobayashi, H.P. Nilles, F. Ploger, S. Raby and M. Ratz, Stringy origin of non-Abelian discrete flavor symmetries, Nucl. Phys. B 768 (2007) 135 [ hep-ph/0611020]

    2007 arXiv

  4. [12]

    F. Beye, T. Kobayashi and S. Kuwakino, Gauge Origin of Discrete Flavor Symmetries in Heterotic Orbifolds, Phys. Lett. B736 (2014) 433 [ 1406.4660]

    2014 arXiv

  5. [13]

    Thorngren and Y

    R. Thorngren and Y. Wang, Fusion category symmetry. Part II. Categoriosities at c = 1 and beyond, JHEP 07 (2024) 051 [ 2106.12577]. – 27 –

    2024 arXiv

  6. [14]

    Heckman, J

    J.J. Heckman, J. McNamara, M. Montero, A. Sharon, C. Vafa and I. Valenzuela, On the Fate of Stringy Non-Invertible Symmetries, 2402.00118

    arXiv

  7. [15]

    Kaidi, Y

    J. Kaidi, Y. Tachikawa and H.Y. Zhang, On a class of selection rules without group actions in field theory and string theory, SciPost Phys. 17 (2024) 169 [ 2402.00105]

    2024 arXiv

  8. [16]

    Kobayashi and H

    T. Kobayashi and H. Otsuka, Non-invertible flavor symmetries in magnetized extra dimensions, JHEP 11 (2024) 120 [ 2408.13984]

    2024 arXiv

  9. [17]

    Funakoshi, T

    S. Funakoshi, T. Kobayashi and H. Otsuka, Quantum aspects of non-invertible flavor symmetries in intersecting/magnetized D-brane models, JHEP 04 (2025) 183 [ 2412.12524]

    2025 arXiv

  10. [18]

    Choi, H.T

    Y. Choi, H.T. Lam and S.-H. Shao, Noninvertible Global Symmetries in the Standard Model, Phys. Rev. Lett.129 (2022) 161601 [ 2205.05086]

    2022 arXiv

  11. [19]

    Cordova, S

    C. Cordova, S. Hong, S. Koren and K. Ohmori, Neutrino Masses from Generalized Symmetry Breaking, Phys. Rev. X 14 (2024) 031033 [ 2211.07639]

    2024 arXiv

  12. [20]

    Cordova and K

    C. Cordova and K. Ohmori, Noninvertible Chiral Symmetry and Exponential Hierarchies, Phys. Rev. X 13 (2023) 011034 [ 2205.06243]

    2023 arXiv

  13. [21]

    Cordova, S

    C. Cordova, S. Hong and S. Koren, Non-Invertible Peccei-Quinn Symmetry and the Massless Quark Solution to the Strong CP Problem, 2402.12453

    arXiv

  14. [22]

    Kobayashi, H

    T. Kobayashi, H. Otsuka and M. Tanimoto, Yukawa textures from non-invertible symmetries, JHEP 12 (2024) 117 [ 2409.05270]

    2024 arXiv

  15. [23]

    Kobayashi, Y

    T. Kobayashi, Y. Nishioka, H. Otsuka and M. Tanimoto, More about quark Yukawa textures from selection rules without group actions, 2503.09966

    arXiv

  16. [24]

    Suzuki and L.-X

    M. Suzuki and L.-X. Xu, Phenomenological implications of a class of non-invertible selection rules, 2503.19964

  17. [25]

    Liang and T.T

    Q. Liang and T.T. Yanagida, Non-invertible symmetry as an axion-less solution to the strong CP problem, 2505.05142

    arXiv

  18. [26]

    Kobayashi, H

    T. Kobayashi, H. Otsuka, M. Tanimoto and H. Uchida, Lepton mass textures from non-invertible multiplication rules, 2505.07262

    arXiv

  19. [27]

    Kobayashi, H

    T. Kobayashi, H. Okada and H. Otsuka, Radiative neutrino mass models from non-invertible selection rules, 2505.14878

  20. [28]

    Farrar and P

    G.R. Farrar and P. Fayet, Phenomenology of the Production, Decay, and Detection of New Hadronic States Associated with Supersymmetry, Phys. Lett. B76 (1978) 575

    1978

  21. [29]

    Dimopoulos and H

    S. Dimopoulos and H. Georgi, Softly Broken Supersymmetry and SU(5), Nucl. Phys. B 193 (1981) 150

    1981

  22. [30]

    Dimopoulos, S

    S. Dimopoulos, S. Raby and F. Wilczek, Proton Decay in Supersymmetric Models, Phys. Lett. B 112 (1982) 133

    1982

  23. [31]

    Ibanez and G.G

    L.E. Ibanez and G.G. Ross, Discrete gauge symmetry anomalies, Phys. Lett. B260 (1991) 291

    1991

  24. [32]

    Ibanez and G.G

    L.E. Ibanez and G.G. Ross, Discrete gauge symmetries and the origin of baryon and lepton number conservation in supersymmetric versions of the standard model, Nucl. Phys. B 368 (1992) 3

    1992

  25. [33]

    Dreiner, C

    H.K. Dreiner, C. Luhn and M. Thormeier, What is the discrete gauge symmetry of the MSSM?, Phys. Rev. D73 (2006) 075007 [ hep-ph/0512163]. – 28 –

    2006 arXiv

  26. [34]

    Abe, K.-S

    H. Abe, K.-S. Choi, T. Kobayashi and H. Ohki, Non-Abelian Discrete Flavor Symmetries from Magnetized/Intersecting Brane Models, Nucl. Phys. B 820 (2009) 317 [ 0904.2631]

    2009 arXiv

  27. [35]

    Berasaluce-Gonzalez, P.G

    M. Berasaluce-Gonzalez, P.G. Camara, F. Marchesano, D. Regalado and A.M. Uranga, Non-Abelian discrete gauge symmetries in 4d string models, JHEP 09 (2012) 059 [1206.2383]

    2012 arXiv

  28. [36]

    Marchesano and J

    F. Marchesano and J. Quirant, A Landscape of AdS Flux Vacua, JHEP 12 (2019) 110 [1908.11386]

    2019 arXiv

  29. [37]

    H. Abe, T. Kobayashi and H. Ohki, Magnetized orbifold models, JHEP 09 (2008) 043 [0806.4748]

    2008 arXiv

  30. [38]

    Barbier et al., R-parity violating supersymmetry, Phys

    R. Barbier et al., R-parity violating supersymmetry, Phys. Rept. 420 (2005) 1 [hep-ph/0406039]

    2005 arXiv

  31. [39]

    Enqvist and A

    K. Enqvist and A. Mazumdar, Cosmological consequences of MSSM flat directions, Phys. Rept. 380 (2003) 99 [ hep-ph/0209244]. – 29 –

    2003 arXiv

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