Pith. sign in

REVIEW 2 major objections 3 minor 1 cited by

Charge quantisation, monopoles and emergent symmetry in the Standard Model and its embeddings

T0 review · 2 major / 3 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read This paper shows that the Standard Model's true gauge group, encoded by two integers (p,k), completely determines electric and magnetic charge quantisation, so a single measured fractional charge would fix the group's global structure.

desk verdict A solid, mostly sound classification of the SM's global structure via (p,k), with a genuinely new SU2Y model, but the advertised one-to-one map from minimal charge to (p,k) fails once negative compositeness degree is allowed, as the authors themselves do. read the letter →

arxiv 2507.01777 v1 pith:K7MCIOM7 submitted 2025-07-02 hep-ph hep-th

Rodrigo Alonso , Despoina Dimakou , Yunji Ha , Valentin V. Khoze This is my paper
classification hep-phhep-th
keywords chargequantisationmonopoleshigher-formsymmetryStandardModelglobalstructurecompositenessdegree'tHooftlines1-formGUTembeddings
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 aims to settle, in principle, how the unknown global (quotient) structure of the Standard Model gauge group governs charge quantisation. It argues that the true group is one of four possibilities $G_p = (SU(3)_c \times SU(2)_L \times U(1)_Y)/\mathbb{Z}_p$, $p = 1,2,3,6$, and that the additional integer $k$ (the compositeness degree) fixes the normalisation of hypercharge. Introducing the charge operator $Q_6$ and its eigenvalue mod 6, the electric hexality $n_6$, the paper shows that all 't Hooft lines (magnetic probes) are labelled by $n_6^m = q_m \bmod 6$, with allowed $q_m$ values set by $p$. The central quantitative claim is that the minimal colour-singlet electric charge and the minimal monopole charge are both $|6/p + 6k|$, so the pair $(p,k)$ fixes the full electric and magnetic lattices. If this is right, any future observation of a single stable fractional colour-singlet charge would uniquely determine the Standard Model's global structure and predict the monopole spectrum.

What carries the argument

The central object is the charge operator $Q_6 = 2\tilde{\lambda}_8 + 3\tilde{T}_{3L} + 6Q_Y$, with tilded generators normalised so that the smallest eigenvalue has modulus one; its eigenvalues $q_6$ are integers, and $n_6 = q_6 \bmod 6$ is the index that classifies electric states. Magnetic states are classified by the conjugate index $n_6^m = q_m \bmod 6$, and the allowed values for each are displayed on a pair of stairway lattices whose periodicity determines $p$. The group-theoretic workhorse is the exact sequence for $G_p = (SU(3)_c \times SU(2)_L \times R_Y)/K_p$ with $K_p \simeq \mathbb{Z}$ acting by $2\pi Q_6/p$ translations, which makes the topology ($\pi_1 = \mathbb{Z}$) independent of $p$; the finer distinction is carried by the 1-form magnetic symmetry $\mathbb{Z}_p^{(1)}$ and electric symmetry $\mathbb{Z}_{6/p}^{(1)}$. Combining the Dirac quantisation condition for 't Hooft lines with the spectrum constraint $6Q_Y + 2n_c + 3n_L = p\mathbb{Z}$ produces the flux solutions (6.12), and the Brandt-Neri conditions (6.21) then fix the unique non-Abelian fluxes for each topological charge.

What would settle it

Measuring the minimal colour-singlet electric charge $1/N$ and the minimal monopole magnetic charge in the same theory and finding they do not both equal $|6/p+6k|$ for the same pair $(p,k)$ — for example, a charge-$1/5$ colour singlet together with a lightest monopole of charge different from 5 — would falsify the central claim. Alternatively, a stable monopole with flux numbers $(n_1,n_2,m;q_m) = (1,0,0;1)$ in a $G_6$ theory would violate the predicted unique flux pattern for $q_m = 1$.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is a complete dictionary between the global structure of the Standard Model gauge group and its charge lattices. For every $p$ the allowed electric states have hexality $n_6 = 2n_c + 3n_L + 6Q_Y \bmod 6$ taking values in $\mathbb{Z}_p$, while the allowed 't Hooft lines have $n_6^m = q_m \bmod 6$ with $q_m \in (6/p)\mathbb{Z}$, and the correlation between the two lattices is displayed by a 'stairway' whose period is $p$. Solving the Dirac quantisation conditions against the spectrum constraint yields, for each $p$, a 4-parameter family of magnetic fluxes; imposing the Brandt-Neri stability conditions selects a unique tower of stable dynamical monopoles $M_{q_m}$ for $q_m = 1,\dots,6$, each present only in the $G_p$ theories that allow that charge. After electroweak symmetry breaking the lattice becomes 3-dimensional with the $SU(2)_L$ fluxes aligned along the photon. With compositeness degree $k$, both the minimal colour-singlet electric charge and the minimal monopole charge equal $|6/p + 6k|$, and the emergent deep-IR electric 1-form symmetry is $\mathbb{Z}_{|6/p+6k|}$.

Load-bearing premise

The stable monopole tower $M_1,\dots,M_6$ rests on the Brandt-Neri stability conditions selecting a unique set of non-Abelian flux numbers for each topological charge $q_m$, before and after electroweak symmetry breaking and in every ultraviolet embedding; if those conditions fail to select a unique flux, the tower is not unique.

Editorial extensions

If this is right

  • If correct, a laboratory observation of any stable colour-singlet with fractional charge $1/N$ immediately identifies $(p,k)$ and therefore predicts the full magnetic spectrum, including which of $M_1,\dots,M_6$ is the lightest monopole.
  • The lightest monopole's charge distinguishes the group: $q=1$ only for $G_6$, $q=2$ for $G_3$, $q=3$ for $G_2$, and $q=6$ for $G_1$ (with $k=0$), so the monopole charge hierarchy is a direct test of the global structure.
  • After electroweak symmetry breaking the $SU(2)_L$ flux of every monopole aligns with the photon, changing the long-range fields and the fermion–monopole scattering predictions compared with the unbroken case.
  • The SU2Y model is an explicit, renormalisable and anomaly-free UV completion of $G_1$ whose new fermions have masses bounded by about $4\pi v$ and carry fractional charges, making the $p=1$ scenario testable at current and future colliders.

Reading between the lines

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

  • Because $|6/p+6k|$ runs bijectively over the positive integers, the inverse-charge measurement alone suffices to identify $(p,k)$, so no monopole observation is necessary in principle to fix the Standard Model's global structure.
  • The same hexality construction should transplant to any gauge theory with a $\mathbb{Z}_N$ centre; dark-sector models with non-trivial global structure would inherit an identical stairway dictionary between electric and magnetic charge lattices.
  • The emergent $\mathbb{Z}_{|6/p+6k|}$ electric 1-form symmetry implies that stable fractional-charge relics of any kind are automatically charged under a discrete symmetry that survives to zero energy, which may connect to searches for exotic millicharged or CHAMP dark matter.
  • If the Brandt-Neri assumption is correct but the UV embeddings differ (e.g. SU(5) versus SO(10)-type hierarchies), the paper's monopole towers still match, so the tower is a robust group-theoretic prediction independent of the GUT-breaking pattern; this robustness is testable by lattice simulations of 't Hooft-Polyakov solutions in each UV model.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 3 minor

Summary. This paper provides a systematic bottom-up analysis of the possible global forms G_p = (SU(3)_c × SU(2)_L × U(1)_Y)/Z_p of the Standard Model gauge group, using the operator Q6(k)=2λ8+3T3L+6(1+pk)QY and the index n6=q6 mod 6. It derives the allowed electric and magnetic spectra for p=1,2,3,6, constructs the associated 1-form symmetries Z_mag(p) and Z_elec(6/p), introduces the compositeness degree k, and extends the analysis to the unbroken SU(3)_c × U(1)_em theory. On the UV side it studies SU(2)_Y, Trinification, Pati–Salam, SU(5), and SU(7) embeddings, proposes a new anomaly-free renormalisable SU(3)_c × SU(2)_L × SU(2)_Y model for the p=1 case, and derives the dynamical monopole spectrum (Tables 14–15) and its k-dependence (Table 16). The central forward claim is that every (p,k) fixes a unique electric/magnetic charge lattice with minimal colour-singlet electric charge and minimal monopole charge equal to |6/p+6k|.

Significance. The group-theoretic framework is clean and the forward derivations are largely convincing: they reproduce the known results for SU(5) (p=6), Pati–Salam (p=3), and Trinification (p=2), and the new SU2Y model provides a concrete non-trivial p=1 embedding with explicit anomaly checks and mass matrices. The derivation of the monopole lattice from Dirac quantisation conditions is transparent and the 'stairway' visualisation is useful. If the issues below are fixed, the paper would be a valuable reference for the global structure of the Standard Model and its embeddings. It should be noted, however, that the advertised inverse use of charge measurements to identify (p,k) uniquely is not supported as stated, because negative compositeness degrees create degeneracies that the manuscript does not resolve.

major comments (2)
  1. [Sec. 5, Eq. (5.22); Sec. 2.3, Eq. (2.76)] The claim that solving D=|6/p+6k| uniquely determines G_p and k is false for negative compositeness degree, which the paper explicitly allows (k∈Z in Eq. (2.50), and negative-k entries appear in Table 16). For example, (p,k)=(2,0) and (2,-1) both give |6/p+6k|=3, so a measured minimal colour-singlet charge 1/3 and minimal monopole charge 3 cannot distinguish them; Table 16 itself lists q_m=-3 for (p,k)=(2,-1), identical in magnitude to the M3 monopole of (p,k)=(2,0). The same degeneracy occurs for p=1 with k=0 and k=-2. In addition, Eq. (2.76) omits the absolute value and is ill-defined for (p,k)=(1,-1), where 6/p+6k=0 and the emergent symmetry Z_{|6/p+6k|} would be Z_0. The forward direction, i.e. that each (p,k) fixes a lattice, is unaffected, but the inverse identification needs either a restriction of k to a canonical range or an explicit statement of the equivalence classes under the reflection k ↔ -2/p - k for p=1,2.
  2. [Sec. 6.2, Eq. (6.21) and Tables 14–15] The statement that for each topological charge q_m the non-Abelian fluxes are completely fixed, and hence that Tables 14 and 15 give the tower of stable monopoles, rests on the Brandt–Neri stability conditions imported from Refs. [46,47,41]. These conditions are assumed to apply unchanged to each of the groups G_p, both before and after electroweak symmetry breaking, and in each UV embedding, but this is not demonstrated in the manuscript. Please provide a verification, or a precise reference for the SM product group and its quotients, that Eq. (6.21) selects a unique flux orbit for every q_m, and clarify how this interacts with the discrete gauge ordering discussed near Eq. (6.17). If more than one stable flux configuration exists for a given q_m, the claimed uniqueness of the M1–M6 tower would need to be weakened.
minor comments (3)
  1. [Throughout] There are several typos and wording issues, including 'T able' in table captions, 'neccesarily', 'apriori', 'straightfoward', and 'rations' in Eq. (4.65); these should be corrected.
  2. [Sec. 4.1, particle count after Eq. (4.9)] The statement 'Particle count: 19 more chiral fermions (times 3 generations) counting only chirality of states and not colour' appears inconsistent with the explicit field listing in Eqs. (4.5)–(4.9); please clarify the counting convention.
  3. [Sec. 6.1, after Eq. (6.17)] The discrete gauge ordering n1 ≥ n2 ≥ 0 and m ≥ 0 is stated as a way to remove degeneracy, but Tables 14 and 15 use negative n1 and n2; please specify that the ordering applies within each Weyl orbit and state how the tabulated representatives are chosen.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the charge and monopole spectra are derived from the group definition and Dirac quantization, with the embeddings used as consistency checks rather than fitted inputs.

full rationale

The paper's derivation chain is self-contained rather than circular. The operator Q6 and the quotient Gp are defined in Eqs. (2.2)-(2.9); the allowed electric indices n6 and magnetic indices nm6 are then obtained by solving periodicity and Dirac quantization conditions (Eqs. (2.9), (6.9)-(6.12)). The magnetic spectrum in Secs. 6-7 is computed from the same spectrum condition together with the Brandt-Neri stability conditions [46,47], and the G6 case is benchmarked against the earlier monopole analyses in Refs. [41,48]. The UV embeddings (SU(5), Pati-Salam, Trinification, SU(3)xSU(2)^2) are not used to fit p or k; instead the paper derives p from the embedding generators via Eq. (3.15) and verifies the resulting lattices against those known models. The compositeness degree k is introduced as a free integer specifying the stairway placement of qL (Eq. (2.50)); the minimal-charge formulas (2.76) and (7.9) are algebraic inverses of that defining rescaling and therefore dictionary relations rather than fitted predictions. The emergent 1-form symmetry is likewise constructed as the kernel of the defining charge assignments, so its dimension is a consequence of the construction, not a fitted output. The paper's claim of a one-to-one (p,k) determination for all integer k is mathematically incorrect for negative k (for example, (p,k)=(2,0) and (2,-1) both give |6/p+6k|=3), but this is a correctness flaw in the inverse use of the formula, not a circularity: the forward statements that each (p,k) fixes a lattice are unaffected. Self-citations (Ref. [17] for k, Ref. [48] for EWSB monopoles) introduce notation and prior context, but the present paper re-derives the relevant constraints from group theory and Dirac quantization, so those citations are not load-bearing evidence for the central claims.

Assumptions & free parameters 2 free parameters · 5 assumptions · 3 invented entities

The core classification rests on the assumed discrete set of quotients G_p, the choice of Q6 as the generator of the quotient, the integer compositeness degree k that rescales hypercharge, and the stability assumptions that select which magnetic probes become dynamical monopoles. None of these are fitted to experimental data; they are structural choices inherited from prior work or introduced to organize the possible charge lattices.

free parameters (2)
  • p
    Order of the quotient in G_p; a discrete choice taking values 1,2,3,6. It is not fitted to data, but each choice defines a different theory and the paper analyzes all four.
  • compositeness degree k
    Integer parameter from Ref. [17] rescaling hypercharge in Q6(k) = 2λ8 + 3T3L + 6(1+pk)QY. Chosen by hand to parameterize possible placements of the quark doublet; no experimental input determines it.
assumptions (5)
  • domain assumption The possible Standard Model gauge groups are exactly G_p = (SU(3)xSU(2)xU(1))/Z_p for p=1,2,3,6.
    Inherited from Refs. [5,6]; the paper does not re-derive the possible quotients, it uses them as the starting classification.
  • ad hoc to paper The quotient Z_p acts via the operator Q6 = 2λ8 + 3T3L + 6QY, imposing n6 = pZ mod 6 on allowed states.
    This is the paper's defining construction (Eq. (2.2), (2.9)); it fixes how the centre is removed and is the basis for all subsequent n6 and n_m^6 predictions.
  • domain assumption All currently known SM fields have n6 = 0.
    Used in Sec. 2.1 to conclude that the present spectrum cannot distinguish the four groups; follows from the SM quantum numbers in Table 1.
  • domain assumption U(1)_Y is embedded in a non-Abelian group that breaks to U(1)_Y via an adjoint Higgs, ensuring finite-energy 't Hooft-Polyakov monopoles.
    Stated in Sec. 6.2 as the basis for dynamical monopoles; it is assumed rather than proved for each of the four embeddings.
  • domain assumption The Brandt-Neri stability conditions Eq. (6.21) fix the non-Abelian flux numbers of stable monopoles.
    Imported from Refs. [46,47]; used in Sec. 6.2 to select the monopoles M1-M6 in Table 14.
invented entities (3)
  • Hexality n6
    purpose: A discrete quantum number labeling electric representations of each G_p; defined as 6QY+2nc+3nL mod 6.
    It is a repackaging of existing charges, not an independent degree of freedom; it carries no falsifiable handle beyond the charge lattice itself.
  • Emergent electric 1-form symmetry Z_emg
    purpose: An infrared symmetry that acts on Wilson lines but is unbroken by any SM state; defined via η in Eq. (2.73).
    The symmetry is constructed from the same charges that define (p,k), so its existence is built into the framework rather than independently testable.
  • SU2Y BSM fermions (U, D, X, L', L'', L''', E', E'', N', N'', N''') independent evidence
    purpose: New chiral fermions required to make the SU(3)xSU(2)xSU(2)_Y embedding of hypercharge anomaly-free and to fill the p=1 spectrum.
    The model predicts stable fractionally charged states with specific n6 values and masses below about 4πv, giving concrete collider and cosmic-ray search targets (c.f. Refs. [27,28,49]).

how reviews work

0 comments
Cite this review

Pith. "Pith review of Charge quantisation, monopoles and emergent symmetry in the Standard Model and its embeddings." pith.science (2026). https://pith.science/paper/K7MCIOM7

@misc{pith2026250701777,
  author       = {Pith},
  title        = {Pith review of: Charge quantisation, monopoles and emergent symmetry in the Standard Model and its embeddings},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/K7MCIOM7}},
  note         = {Machine review of arXiv:2507.01777}
}
abstract

This work studies the connection of the global properties of the SM gauge group to 1-form discrete symmetries, the possible non-Abelian embeddings of the SM group, and electric and magnetic charge quantisation. Building on previous work, we introduce indexes to characterise the group choices, connect the concept of compositeness degree to emergent electric 1-form symmetry, introduce a new model to fill in the $p=1$ gap, and analyse the magnetic spectrum while connecting its UV and IR realisations.

Discussion (0). Sign in to comment.

Forward citations

Cited by 1 Pith paper

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

  1. Phenomenology of Fractionally Charged Particles: Two Reps Are Better Than One

    hep-ph 2025-07 accept novelty 6.0 of 10

    Adding a second fractionally charged particle can weaken existing LHC bounds on the heavy partner by factors of a few while boosting production of the light partner by up to three orders of magnitude, motivating new i...

Reference graph

Works this paper leans on

56 extracted references · 24 canonical work pages · cited by 1 Pith paper

  1. [1]

    Anber and E

    M.M. Anber and E. Poppitz, Nonperturbative effects in the Standard Model with gauged 1-form symmetry , JHEP 12 (2021) 055 [ 2110.02981]

    arXiv 2021

  2. [2]

    Langacker and G

    P. Langacker and G. Steigman, Requiem for an FCHAMP? Fractionally CHArged, Massive Particle, Phys. Rev. D 84 (2011) 065040 [ 1107.3131]

    arXiv 2011

  3. [3]

    Hannestad, What is the lowest possible reheating temperature? , Phys

    S. Hannestad, What is the lowest possible reheating temperature? , Phys. Rev. D 70 (2004) 043506 [astro-ph/0403291]

    arXiv 2004

  4. [4]

    de Salas, M

    P.F. de Salas, M. Lattanzi, G. Mangano, G. Miele, S. Pastor and O. Pisanti, Bounds on very low reheating scenarios after Planck , Phys. Rev. D 92 (2015) 123534 [ 1511.00672]

    arXiv 2015

  5. [5]

    Hucks, Global structure of the standard model, anomalies, and charge quantization , Phys

    J. Hucks, Global structure of the standard model, anomalies, and charge quantization , Phys. Rev. D 43 (1991) 2709

    work page 1991

  6. [6]

    Tong, Line Operators in the Standard Model , JHEP 07 (2017) 104 [ 1705.01853]

    D. Tong, Line Operators in the Standard Model , JHEP 07 (2017) 104 [ 1705.01853]

    arXiv 2017

  7. [7]

    Wilson, Confinement of Quarks , Phys

    K.G. Wilson, Confinement of Quarks , Phys. Rev. D 10 (1974) 2445

    1974

  8. [8]

    ’t Hooft, On the Phase Transition Towards Permanent Quark Confinement , Nucl

    G. ’t Hooft, On the Phase Transition Towards Permanent Quark Confinement , Nucl. Phys. B 138 (1978) 1

    work page 1978

Show all 56 references
  1. [9]

    Aharony, N

    O. Aharony, N. Seiberg and Y. Tachikawa, Reading between the lines of four-dimensional gauge theories, JHEP 08 (2013) 115 [ 1305.0318]

    2013 arXiv

  2. [10]

    Gaiotto, A

    D. Gaiotto, A. Kapustin, N. Seiberg and B. Willett, Generalized Global Symmetries, JHEP 02 (2015) 172 [ 1412.5148]

    2015 arXiv

  3. [11]

    Dirac, Quantised singularities in the electromagnetic field , Proc

    P.A.M. Dirac, Quantised singularities in the electromagnetic field , Proc. Roy. Soc. Lond. A 133 (1931) 60

    1931

  4. [12]

    Wu and C.N

    T.T. Wu and C.N. Yang, Concept of Nonintegrable Phase Factors and Global Formulation of Gauge Fields , Phys. Rev. D 12 (1975) 3845

    1975

  5. [13]

    Brennan and S

    T.D. Brennan and S. Hong, Introduction to Generalized Global Symmetries in QFT and Particle Physics , 2306.00912

    arXiv

  6. [14]

    Cordova, T.T

    C. Cordova, T.T. Dumitrescu, K. Intriligator and S.-H. Shao, Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond , in Snowmass 2021 , 5, 2022 [2205.09545]

    2021 arXiv

  7. [15]

    McGreevy, Generalized Symmetries in Condensed Matter , Ann

    J. McGreevy, Generalized Symmetries in Condensed Matter , Ann. Rev. Condensed Matter Phys. 14 (2023) 57 [ 2204.03045]

    2023 arXiv

  8. [16]

    Bhardwaj, L.E

    L. Bhardwaj, L.E. Bottini, L. Fraser-Taliente, L. Gladden, D.S.W. Gould, A. Platschorre et al., Lectures on generalized symmetries, Phys. Rept. 1051 (2024) 1 [ 2307.07547]

    2024 arXiv

  9. [17]

    Alonso, D

    R. Alonso, D. Dimakou and M. West, Fractional-charge hadrons and leptons to tell the Standard Model group apart , Phys. Lett. B 863 (2025) 139354 [ 2404.03438]

    2025 arXiv

  10. [18]

    Koren and A

    S. Koren and A. Martin, Fractionally charged particles at the energy frontier: The SM gauge group and one-form global symmetry , SciPost Phys. 18 (2025) 004 [ 2406.17850]

    2025 arXiv

  11. [19]

    S.H. C. C´ ordova and L. Wang,Axion Domain Walls, Small Instantons, and Non-Invertible Symmetry Breaking, 2309.05636

    arXiv

  12. [20]

    ’t Hooft, Magnetic Monopoles in Unified Gauge Theories , Nucl

    G. ’t Hooft, Magnetic Monopoles in Unified Gauge Theories , Nucl. Phys. B 79 (1974) 276

    1974

  13. [21]

    Polyakov, Particle Spectrum in Quantum Field Theory , JETP Lett

    A.M. Polyakov, Particle Spectrum in Quantum Field Theory , JETP Lett. 20 (1974) 194. – 71 –

    1974

  14. [22]

    Gross and R

    D.J. Gross and R. Jackiw, Effect of anomalies on quasirenormalizable theories , Phys. Rev. D 6 (1972) 477

    1972

  15. [23]

    Weinberg, The quantum theory of fields

    S. Weinberg, The quantum theory of fields. Vol. 2: Modern applications , Cambridge University Press (8, 2013), 10.1017/CBO9781139644174

    2013 doi

  16. [24]

    Witten, An SU(2) Anomaly , Phys

    E. Witten, An SU(2) Anomaly , Phys. Lett. B 117 (1982) 324

    1982

  17. [25]

    Wang, X.-G

    J. Wang, X.-G. Wen and E. Witten, A New SU(2) Anomaly , J. Math. Phys. 60 (2019) 052301 [1810.00844]

    2019 arXiv

  18. [26]

    Davighi, B

    J. Davighi, B. Gripaios and N. Lohitsiri, Global anomalies in the Standard Model(s) and Beyond, JHEP 07 (2020) 232 [ 1910.11277]

    2020 arXiv

  19. [27]

    ATLAS collaboration, Search for heavy charged long-lived particles in the ATLAS detector in 36.1 fb −1 of proton-proton collision data at √s = 13 TeV, Phys. Rev. D 99 (2019) 092007 [1902.01636]

    2019 arXiv

  20. [28]

    CMS collaboration, Search for Fractionally Charged Particles in Proton-Proton Collisions at s=13 TeV, Phys. Rev. Lett. 134 (2025) 131802 [ 2402.09932]

    2025 arXiv

  21. [29]

    ’t Hooft, Symmetry Breaking Through Bell-Jackiw Anomalies , Phys

    G. ’t Hooft, Symmetry Breaking Through Bell-Jackiw Anomalies , Phys. Rev. Lett. 37 (1976) 8

    1976

  22. [30]

    Belavin, A.M

    A.A. Belavin, A.M. Polyakov, A.S. Schwartz and Y.S. Tyupkin, Pseudoparticle Solutions of the Yang-Mills Equations , Phys. Lett. B 59 (1975) 85

    1975

  23. [31]

    ’t Hooft, Computation of the Quantum Effects Due to a Four-Dimensional Pseudoparticle, Phys

    G. ’t Hooft, Computation of the Quantum Effects Due to a Four-Dimensional Pseudoparticle, Phys. Rev. D 14 (1976) 3432

    1976

  24. [32]

    Kuzmin, V.A

    V.A. Kuzmin, V.A. Rubakov and M.E. Shaposhnikov, On the Anomalous Electroweak Baryon Number Nonconservation in the Early Universe , Phys. Lett. B 155 (1985) 36

    1985

  25. [33]

    De R´ ujula, H

    A. De R´ ujula, H. Georgi and S.L. Glashow, Trinification of All Elementary Particle Forces , in Fifth Workshop on Grand Unification , 7, 1984

    1984

  26. [34]

    Babu, X.-G

    K.S. Babu, X.-G. He and S. Pakvasa, Neutrino Masses and Proton Decay Modes in SU (3) × SU (3) × SU (3) Trinification, Phys. Rev. D 33 (1986) 763

    1986

  27. [35]

    Hetzel and B

    J. Hetzel and B. Stech, Low-energy phenomenology of trinification: an effective left-right-symmetric model, Phys. Rev. D 91 (2015) 055026 [ 1502.00919]

    2015 arXiv

  28. [36]

    Georgi and S.L

    H. Georgi and S.L. Glashow, Unity of All Elementary Particle Forces , Phys. Rev. Lett. 32 (1974) 438

    1974

  29. [37]

    Li and F

    L.F. Li and F. Wilczek, Price of Fractionally Charged Particles in a Unified Model , Phys. Lett. B 107 (1981) 64

    1981

  30. [38]

    Farhi and L

    E. Farhi and L. Susskind, A Technicolored G.U.T., Phys. Rev. D 20 (1979) 3404

    1979

  31. [39]

    Umemura and K

    I. Umemura and K. Yamamoto, Symmetry Breaking Patterns in an SU(7) Grand Unified Model, Prog. Theor. Phys. 66 (1981) 1430

    1981

  32. [40]

    Corrigan and D.I

    E. Corrigan and D.I. Olive, Color and Magnetic Monopoles , Nucl. Phys. B 110 (1976) 237

    1976

  33. [41]

    van Beest, P

    M. van Beest, P. Boyle Smith, D. Delmastro, R. Mouland and D. Tong, Fermion-Monopole Scattering in the Standard Model , 2312.17746

    arXiv

  34. [42]

    Dokos and T.N

    C.P. Dokos and T.N. Tomaras, Monopoles and Dyons in the SU(5) Model , Phys. Rev. D 21 (1980) 2940. – 72 –

    1980

  35. [43]

    Gardner and J.A

    C.L. Gardner and J.A. Harvey, Stable Grand Unified Monopoles With Multiple Dirac Charge , Phys. Rev. Lett. 52 (1984) 879

    1984

  36. [44]

    Preskill, Magnetic Monopoles, Ann

    J. Preskill, Magnetic Monopoles, Ann. Rev. Nucl. Part. Sci. 34 (1984) 461

    1984

  37. [45]

    Lubkin, Geometric definition of gauge invariance , Annals Phys

    E. Lubkin, Geometric definition of gauge invariance , Annals Phys. 23 (1963) 233

    1963

  38. [46]

    Brandt and F

    R.A. Brandt and F. Neri, Stability Analysis for Singular Nonabelian Magnetic Monopoles , Nucl. Phys. B 161 (1979) 253

    1979

  39. [47]

    Coleman, The Magnetic Monopole Fifty Years Later , in Les Houches Summer School of Theoretical Physics: Laser-Plasma Interactions , pp

    S.R. Coleman, The Magnetic Monopole Fifty Years Later , in Les Houches Summer School of Theoretical Physics: Laser-Plasma Interactions , pp. 461–552, 6, 1982

    1982

  40. [48]

    Khoze, Monopoles and fermions in the Standard Model , JHEP 09 (2024) 146 [2405.18689]

    V.V. Khoze, Monopoles and fermions in the Standard Model , JHEP 09 (2024) 146 [2405.18689]

    2024 arXiv

  41. [49]

    Dunsky, L.J

    D. Dunsky, L.J. Hall and K. Harigaya, CHAMP Cosmic Rays , JCAP 07 (2019) 015 [1812.11116]

    2019 arXiv

  42. [50]

    Perl, E.R

    M.L. Perl, E.R. Lee and D. Loomba, Searches for fractionally charged particles , Ann. Rev. Nucl. Part. Sci. 59 (2009) 47

    2009

  43. [51]

    MoEDAL collaboration, Magnetic Monopole Search with the Full MoEDAL Trapping Detector in 13 TeV pp Collisions Interpreted in Photon-Fusion and Drell-Yan Production , Phys. Rev. Lett. 123 (2019) 021802 [ 1903.08491]

    2019 arXiv

  44. [52]

    IceCube collaboration, Search for non-relativistic Magnetic Monopoles with IceCube , Eur. Phys. J. C 74 (2014) 2938 [ 1402.3460]

    2014 arXiv

  45. [53]

    IceCube collaboration, Search for Relativistic Magnetic Monopoles with Eight Years of IceCube Data, Phys. Rev. Lett. 128 (2022) 051101 [ 2109.13719]

    2022

  46. [54]

    NOvA collaboration, Search for slow magnetic monopoles with the NOvA detector on the surface, Phys. Rev. D 103 (2021) 012007 [ 2009.04867]

    2021 arXiv

  47. [55]

    Super-Kamiokande collaboration, Search for GUT monopoles at Super–Kamiokande , Astropart. Phys. 36 (2012) 131 [ 1203.0940]

    2012 arXiv

  48. [56]

    Candela, V.V

    P.M. Candela, V.V. Khoze and J. Turner, Monopoles at Future Neutrino Detectors , 2504.14918. – 73 –

    arXiv

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.