Pith. sign in

REVIEW 3 major objections 4 minor 39 references

SL(2N,C) Yang-Mills Theories: Direct Internal Forces and Emerging Gravity

T0 review · 3 major / 4 minor · reviewed 2026-08-03 · deepseek-v4-flash

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

Pith's one-line read This paper proposes that gravity and all internal forces share one local symmetry, SL(2N,C), which a dynamical tetrad condenses down to Lorentz plus SU(N), with Einstein-Cartan gravity generated radiatively from fermion loops.

desk verdict Serious, internally consistent speculative hyperunification whose two headline results—radiative Einstein–Cartan gravity and N=8 with three families—rest on an uncomputed loop coefficient and partly assumed anomaly-matching inputs. read the letter →

arxiv 2511.19210 v6 pith:T6H7VBSJ submitted 2025-11-24 hep-th gr-qchep-ph

J. L. Chkareuli This is my paper · ORCID
classification hep-thgr-qchep-ph MSC 81T1383C4581V22 PACS 04.60.-m12.10.-g11.15.-q
keywords SL(2NC)gaugetheoryhyperunificationemergentgravitytetradcondensationEinstein-Cartanpreonanomalymatchingthreegenerations
topics Yang-Mills Mass Gap
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 tries to establish that gravity need not be put in by hand: it can emerge as a radiative effect from an ordinary Yang-Mills theory with gauge group SL(2N,C). The key step is treating the tetrad — the field that ties spinors to spacetime — as a dynamical field with a fixed-length constraint. The constraint forces the tetrad to acquire a vacuum value that breaks SL(2N,C) down to SL(2,C)×SU(N), leaving a massless graviton and massless SU(N) gauge bosons, while all axial-vector and tensor partners become heavy. The Einstein-Cartan curvature term is then claimed to be generated by fermion one-loop bubbles, tying the Planck scale to the same matter sector that sets the unified gauge coupling. On the matter side, quarks and leptons are proposed to be preon composites, and 't Hooft anomaly matching for three-preon states picks out N=8, yielding three families from SL(16,C) → SL(2,C)×SU(8).

What carries the argument

The dynamical tetrad multiplet e_μ^{aK}, promoted to a gauge field of the inhomogeneous group ISL(2N,C) and subject to the nonlinear sigma-model length constraint (48). Its condensation implements the symmetry breaking and filters the low-energy spectrum. The ghost-free Neville combination of curvature-squared terms fixes the quadratic gauge sector with a single coupling. The fermion-bubble diagrams with V_T and V_e insertions reconstruct the Einstein-Cartan term. The anomaly-matching equation 3 = N²/2 − 7N/2 − 1, whose unique solution N=8 selects SL(16,C).

What would settle it

Evaluate the one-loop integral for the two fermion-bubble diagrams with vertices (61); the claimed emergent Einstein-Cartan term requires a nonzero, positive coefficient proportional to N_f m_ψ² (or N_f Λ²). If a direct calculation gives zero or the wrong sign, the emerging-gravity claim fails.

Watch

Extended reading notes

Core claim

The central claim is that a four-dimensional SL(2N,C) gauge theory, with a universal quadratic Yang-Mills action and a dynamical tetrad obeying the nonlinear length constraint (1/4 e_μ^{aK} e^{μK}_a = M²), is dynamically consistent only after spontaneous symmetry breaking. The tetrad VEV selects a hyperflavor-blind vacuum, breaking SL(2N,C) → SL(2,C)×SU(N), and the ghost-free Neville-type curvature-squared Lagrangian propagates only the massless SU(N) vectors plus a singlet tensor connection, the graviton. A tree-level Einstein-Cartan term is not required: fermion loops involving tetrad and tensor insertions induce e∧e∧R[T] with a coefficient N_f m_ψ²/(16π²) or N_f Λ²/(16π²), so the Planck m

Load-bearing premise

The linchpin is the uncomputed one-loop fermion-bubble coefficient that is asserted to generate the Einstein-Cartan term; if that integral vanishes, changes sign, or mixes differently with curvature-squared terms, gravity is not emergent in the way claimed.

Editorial extensions

If this is right

  • Below the breaking scale the theory is Einstein-Cartan gravity plus SU(N) gauge theory with a single gauge coupling.
  • Axial-vector and tensor gauge fields acquire masses of order gM and decouple, so no new long-range forces appear.
  • The Planck mass is radiatively determined by the fermion mass spectrum or the UV cutoff, not set by a bare parameter.
  • The composite picture predicts three quark-lepton generations and a family symmetry SU(3)_F, with extra composite states potentially observable if M and Λ_MC are below M_Pl.
  • No extra dimensions or string degrees of freedom are needed; unification is purely four-dimensional.

Reading between the lines

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

  • If the one-loop coefficient in Eqs. (62)-(63) is eventually computed and found to be finite and positive, the framework predicts a quantitative relation between the number and masses of heavy vectorlike fermions and Newton's constant; that relation is currently an assertion, not a derivation.
  • The same tetrad-condensation mechanism could be applied to other noncompact groups (e.g., SO(2N,C)) to see if the lifting of noncompact directions is generic; the paper does not explore this.
  • The N=8 selection would be falsified if a richer confined composite spectrum (e.g., five-preon or higher-spin massless composites) also satisfies anomaly matching; testing this requires a dynamical calculation of the composite spectrum, which the paper does not provide.
  • If M and Λ_MC are near the TeV scale, the heavy axial-vector trio could be searched for as Z' -like resonances with distinctive parity-violating couplings; the paper leaves this phenomenological window open.
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

3 major / 4 minor

Summary. The paper develops an SL(2N,C) Yang–Mills-type unification of gravity and internal interactions. It promotes the tetrad to a dynamical multiplet with a nonlinear length constraint (Eq. (48)), argues that a Coleman–Weinberg potential selects a hyperflavor-blind vacuum, and claims that tetrad condensation spontaneously breaks SL(2N,C) to SL(2,C)×SU(N), leaving only the neutral tetrad and SU(N) vectors massless. A ghost-free Neville-type curvature-squared Lagrangian is embedded in the hyperunified quadratic sector (Sec. 3). The Einstein–Cartan term is asserted to be generated radiatively by fermion bubbles (Sec. 5.2, Eqs. (61)–(63)). In the matter sector, the paper proposes that quarks and leptons are composites of SL(2N,C) preons, and uses 't Hooft anomaly matching with three-preon composites to single out N=8, leading to three composite families via SU(8)→SU(5)×SU(3)_F decomposition (Sec. 6.3). The technical core is a consistent group-theoretic exercise, but the load-bearing dynamical steps are asserted rather than computed.

Significance. If the central dynamical claims held, the paper would offer an interesting four-dimensional gauge origin for the Einstein–Cartan term and a natural embedding of SU(N) hyperflavor in SL(2N,C). The treatment of the quadratic curvature sector, the use of dynamical tetrad condensation, and the attempt to derive a preferred N=8 metaflavor group are genuinely ambitious and connect to older hyperunification ideas. It is also a strength that the algebraic decomposition in Sec. 3 is explicit enough to be checked, and that the matter-sector anomaly-matching calculation is presented in a compact, falsifiable form. However, the significance is currently limited by the fact that the two most important results—the radiative emergence of the Einstein–Cartan term and the uniqueness of N=8 with three families—rest on unverified or partly input assumptions. The paper does not yet establish its headline claims; it formulates a coherent scenario whose central quantitative steps remain to be supplied.

major comments (3)
  1. [Sec. 5.2, Eqs. (61)–(63)] The one-loop generation of e∧e∧R[T] is the load-bearing step for emergent gravity, but no loop integral is evaluated. The displayed vertices are schematic: starting from the actual interaction (25), the neutral-tensor vertex involves an anticommutator with the tetrad, {γ^a,γ^{ab}}, not simply γ^c γ^{ab}, so the diagram set and their contractions are underspecified. The gamma-matrix algebra could produce a parity-odd Holst-type contribution as well as the parity-even Einstein–Cartan term, and the relative coefficient of the dT and gT∧T pieces is not checked. If the coefficient vanishes, has the wrong sign, or does not arrange into a gauge-covariant R[T], the relation M_Pl^2 ~ N_f m_ψ^2 (or N_f Λ^2) fails. Equations (62)–(63) are order-of-magnitude estimates, not derived results; a direct one-loop calculation is required.
  2. [Sec. 6.3, Eqs. (70)–(75)] The claimed uniqueness of N=8 and the three-family prediction are not independent consequences. Equation (70) is written with n=3 preons of a given chirality, so the left-hand side of Eq. (72) is input, not output. The integer 3 in Eq. (73) is this preon number. Moreover, the 'three families' in Eq. (75) arise from the SU(3) factor of the SU(5)×SU(3) decomposition of the 216 of SU(8); that SU(3) is inserted as a family symmetry, and the 216 representation is selected by assumptions (i)–(iii) that only three-preon, spin-1/2, single-irrep composites remain massless. Without those assumptions, Eq. (70) has many solutions. The footnote introducing an arbitrary integer p further weakens the uniqueness: the constraint is then n−p=3, so the preferred N=8 depends on choosing n and p, not on anomaly matching alone.
  3. [Sec. 4.2, Eqs. (53)–(57)] The Coleman–Weinberg selection of the hyperflavor-blind vacuum is asserted rather than demonstrated. For the vector sector the statement that 'for any other orientation some m_n^2 become positive' is plausible for H not proportional to identity, but it is not proven, and the axial/tensor contribution is given only schematically in Eq. (56). The central quantitative claim—that the symmetric adjoint tetrad modes receive positive mass squared M^2 ∼ g^4 M^2/(16π^2)—is presented as a dimensional estimate with no calculation. Since this mass matrix is what removes the unwanted hyperflavored tetrad modes and justifies the low-energy spectrum, it is a load-bearing step that needs a real loop computation, including the sign of the effective potential.
minor comments (4)
  1. [Sec. 2.2, Eq. (17)–(19)] The reduction of the general tetrad to the purely vectorial form (19) via the auxiliary multiplet S is described in one sentence. Since the axial tetrad component is central to the later breaking pattern, a more explicit treatment would help.
  2. [Sec. 4.2, counting paragraph] The mode-counting sentence 'this leaves 9N^2 + 1 symmetric traceless modes: 9(N^2−1) in the SU(N) adjoint and 10 in the singlet sector' is ambiguous: 9(N^2−1)+10 is not 9N^2+1 for N≠1. The counting should be rephrased with explicit N-dependence.
  3. [Footnote 3] The parameter p is introduced without definition of which one-preon composites are allowed and without explaining why n−p=3 is required. The footnote appears to weaken the uniqueness claim made in the main text and should be reconciled with Sec. 6.3.
  4. [General] There are a number of small errors and stylistic issues: 'Phys. Review D' in Ref. [16], the reference to 'Percacci' in Ref. [32] should include initials, and the notation ε_k · M^2 · ε_k in Eq. (57) is not defined. The paper would also benefit from a table listing the three scales M, M_Pl, and Λ_MC and the assumed hierarchy.

Circularity Check

2 steps flagged · score 7.0 of 10

Three-family count is inserted as n=3 before the anomaly matching, and the universal-cutoff Planck scale is an assumed input, so the main predictions reduce to inputs.

  1. fitted input called prediction [Sec. 6.3, Eqs. (70)-(75)]
    "the AM condition takes the form n a(N) = sum_r i_r a(r), (70) where n is the number of preons of a given chirality. ... imposing (70) with n=3, a(N)=1, and i_r=1 for a single composite representation r=r_0 yields 3=a(r_0). (72) ... 3 = N^2/2 - 7N/2 -1, N=8, (73) ... 216_{L,R} = [(5+10,3) + (45,1) + (5,8+1) + (24,3) + (1,3) + (1,6)] ... where (5+10,3)_L corresponds precisely to three generations."

    The number 3 that selects N=8 in Eq. (73) is exactly the input n=3 imposed in Eq. (70), and the same 3 reappears in Eq. (75) as the SU(3)_F factor describing 'three generations.' Thus the three-family result is not derived from anomaly matching; it is put in by hand as n=3. The paper's own definition says n is the number of preons of a given chirality, and in its setup there are N left-handed preons, so a natural choice would be n=N rather than n=3. With n=3, Eq. (73) is a consistency condition that manufactures the desired answer, and the 'three generations' in (75) is the same 3 that was inserted in (70).

  2. self definitional [Sec. 5.1-5.2, Eqs. (62)-(63)]
    "In a 'universal cutoff' scenario, if gravity or some UV completion provides a physical cutoff Λ∼M_Pl for all loop integrals, even light fermions induce an Einstein–Cartan term of order N_f Λ^2; this is regulator-dependent but fixes the correct overall scale. ... L_EC^(c) ∼ N_f/(16π^2) Λ^2 e∧e∧R[T], (63) ... with the Planck scale determined by the UV boundary condition set by the UV completion."

    In this scenario the target quantity M_Pl is the input cutoff: Λ∼M_Pl is assumed, and Eq. (63) then returns M_Pl^2 ∼ N_f Λ^2. The 'emergent' gravitational scale is therefore the very scale that was inserted as the regulator. The threshold scenario has the same structural issue when vectorlike fermions are taken near the Planck scale, m_ψ∼M_Pl, so Eq. (62) becomes M_Pl^2 ∼ N_f m_ψ^2 with the Planck scale on both sides. The section describes a scale-setting relation rather than an independent derivation of the Planck mass.

full rationale

The two load-bearing predictive claims are the emergent Einstein–Cartan term and the N=8 three-family composite spectrum. The matter-sector claim is circular in a direct, quotable way: the paper fixes n=3 in the anomaly-matching equation, uses that 3 to solve for N=8, and then identifies the same 3 as the SU(3)_F family-triplet factor producing three generations. The gravitational-sector claim is not a derived prediction in the universal-cutoff scenario because the cutoff is already taken to be M_Pl; Eq. (63) reinstates the Planck scale as an input. The threshold scenario similarly assumes Planck-mass fermions. The uncomputed one-loop coefficient in Sec. 5.2 is a significant gap, but it is not itself a circularity; it is an omitted calculation. Other elements, such as the Neville-type ghost-free quadratic Lagrangian and the tetrad-condensation breaking pattern, are not circular: they are explicit constructions with stated assumptions. The self-citations to [26] for the preon framework are not by themselves load-bearing circularity, since the anomaly matching condition used here is written out in the paper; the circularity lies in the hand-set n=3 and the use of M_Pl as the UV scale.

Assumptions & free parameters 10 free parameters · 8 assumptions · 5 invented entities

The central claims rest on several hand-placed scales (M, Λ_MC, m_ψ, M_LR, M_F), an ad-hoc tetrad length constraint, assumed positivity of a schematic CW potential, an uncomputed one-loop EC coefficient, and preon/massless-composite assumptions. The pure group-theoretic trace algebra and the anomaly-matching arithmetic are standard; the physical inputs are chosen rather than derived.

free parameters (10)
  • Tetrad condensation scale M
    Introduced via the rescaling e_μ^{aK} = M E_μ^{aK} and the constraint (48); sets the SL(2N,C) breaking scale and all heavy gauge-boson masses ~gM. No dynamical origin is given.
  • Curvature-squared coupling λ_I = λ_I = -2/3
    Chosen to normalize the vector/axial sectors canonically and to reproduce the Neville ghost-free combination (43); fixed by convention rather than derived.
  • Planck scale / UV cutoff Λ = Λ ~ M_Pl
    In the universal-cutoff scenario (Eq. (63)), the generated Einstein–Cartan coefficient is N_f Λ² with Λ ~ M_Pl; the result being derived therefore enters as an input.
  • Heavy vectorlike fermion mass m_ψ = m_ψ ~ M_Pl
    In the threshold scenario (Eq. (62)), M_Pl² ∝ N_f m_ψ²; the Planck scale is fixed by assuming m_ψ ~ M_Pl, again an input.
  • Number of heavy species N_f
    Multiplicity controlling the induced Planck mass; no value or constraint is given.
  • Metacolor confinement scale Λ_MC
    Scale at which preons confine into composites; free parameter controlling the composite spectrum and Yukawa couplings.
  • L-R breaking scale M_LR / family scale M_F
    VEV scale in the Φ' potential (76)/(78) that breaks SU(8)_R to SU(5)×SU(3)_F; the hierarchy M_F vs M_SM is left open.
  • Yukawa coefficients a_U,D, b_U,D = order 1
    Dimensionless couplings in Eq. (84); not predicted, just assumed to be of order unity.
  • Generalized AM parameter p = p = n - 3
    Footnote 3: the generalized anomaly condition adds p one-preon composites; any n with n-p=3 works, so the uniqueness of N=8 is maintained only by keeping their difference fixed—the parameter itself is unconstrained.
  • LR potential parameters h1,h2,h3,M_U = h3 > 2(h1+h2)
    Parameters of the L-R breaking potential (76); chosen by hand to produce the asymmetric VEV (78).
assumptions (8)
  • ad hoc to paper The tetrad can be promoted to a dynamical field with a nonlinear sigma-model length constraint (1/4 e_μ^{aK} e^{μK}_a = M²)
    Central premise of the SSB mechanism (Sec. 4.1, Eq. (48)); no underlying dynamics generates this constraint.
  • domain assumption The Neville ghost-free curvature-squared combination (a=15/4, b=-1, c=1/8) is the correct quadratic Lagrangian for the full SL(2N,C) tensor sector
    Taken from the SL(2,C) literature [12,13] and enforced by Eq. (43); no independent derivation for the SL(2N,C) case is given.
  • ad hoc to paper The Coleman–Weinberg potential from vector, axial, and tensor loops selects the hyperflavor-blind vacuum and gives positive mass to all symmetric adjoint tetrad modes
    Eqs. (53)–(57) summarize the claim; the actual CW calculation is not shown and positivity is asserted.
  • ad hoc to paper Fermion loops with vertices (61) generate exactly the Einstein–Cartan term e∧e∧R[T] with the stated coefficient
    The core of 'emerging gravity' (Sec. 5.2); the loop computation is not performed.
  • domain assumption Preons are confined by an SO(n)_L × SO(n)_R metacolor gauge group with comparable left/right scales and produce massless composite fermions
    Borrowed from [26]; necessary for the anomaly-matching framework of Sec. 6.2.
  • ad hoc to paper Only three-preon spin-1/2 composites in a single irreducible representation of SU(N) remain massless (assumptions (i)–(iii))
    This restriction selects the mixed tensor Ψ^i_[jk] and forces N=8 in Eq. (73).
  • standard math Standard trace identities for Dirac and SU(N) matrices used in Sec. 3
    Background linear algebra; not an issue.
  • domain assumption 't Hooft anomaly matching is applicable to the chiral SU(N)_L × SU(N)_R preon symmetry
    Standard technique, used in Sec. 6.3.
invented entities (5)
  • Dynamical tetrad multiplet e_μ^{aK} with hyperflavor components
    purpose: Triggers SSB of SL(2N,C) and defines spacetime metric; hyperflavored modes become heavy or are eaten.
    Extension of the ordinary tetrad to the SL(2N,C) structure; no observable beyond the standard tetrad is predicted at low energy.
  • Heavy axial-vector A^k_μ and tensor T^{abK}_μ gauge multiplets
    purpose: Gauge partners in SL(2N,C); masses ~gM after tetrad condensation; expected to decouple at high scale.
    No definite mass prediction because M is free; only qualitative heavy-state existence is claimed.
  • Preons P^α_{iaL}, Q^α'_{iaR}
    purpose: Fundamental chiral constituents whose bound states are quarks and leptons; carry SL(2N,C) metaflavor and SO(n) metacolor.
    No direct detection or predicted observable below Λ_MC; the model is built to make them invisible at low energies.
  • Metacolor gauge group SO(n)_L × SO(n)_R
    purpose: Confinement force that binds preons into massless composites.
    A new strong interaction with unconstrained n and scale Λ_MC; no signature is specified.
  • Scalar multiplets Φ', Σ, H, ξ, χ
    purpose: Break L-R, SU(8), SU(5), SU(3)_F, and generate Yukawa textures.
    Introduced ad hoc; the VEVs (78) are assumed and the multiplet content is prescribed to produce the desired breaking.

how reviews work

0 comments
Cite this review

Pith. "Pith review of SL(2N,C) Yang-Mills Theories: Direct Internal Forces and Emerging Gravity." pith.science (2026). https://pith.science/paper/T6H7VBSJ

@misc{pith2026251119210,
  author       = {Pith},
  title        = {Pith review of: SL(2N,C) Yang-Mills Theories: Direct Internal Forces and Emerging Gravity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/T6H7VBSJ}},
  note         = {Machine review of arXiv:2511.19210}
}
abstract

A four-dimensional gauge-gravity unification based on local $SL(2N,C)$ symmetry is developed in a universal Yang--Mills-type setting, which, however, appears dynamically consistent only in the symmetry-broken phase. In the exact symmetry limit the theory may only be formulated in a premetric framework, where the accompanying tetrad multiplets, though promoted to dynamical fields, do not yet satisfy the conventional invertibility conditions. An ordinary Einstein--Cartan spacetime geometry emerges only in the broken post-soldering phase, in which the $SL(2N,C)$ tetrad multiplets are treated as constrained dynamical fields selecting a neutral internal symmetry branch. This realizes the breaking $SL(2N,C)\to SL(2,C)\times SU(N)$, thereby lifting all noncompact internal directions, while the surviving neutral tetrad is, as usual, associated with the gravitational field. A special ghost-free curvature-squared Lagrangian provides a consistent quadratic sector for the spin connection, propagating only admissible connection modes: the massless $SU(N)$ vector fields together with massive axial-vector and pseudoscalar multiplets. The Einstein--Cartan linear curvature term is argued to arise radiatively from fermion loops, thereby relating the gravitational scale to the same $SL(2N,C)$-covariant matter sector that defines the unified gauge coupling. Finally, the matter sector points to a deeper elementarity of $SL(2N,C)$ spinors, identified with preon constituents whose bound states form the observed quarks and leptons. Anomaly matching between preons and composites singles out $N=8$. The chain $SL(16,C)\to SL(2,C)\times SU(8)$ then naturally yields three composite quark--lepton families, while filtering out extraneous heavy states.

Figures

Figures reproduced from arXiv: 2511.19210 by the authors.

Figure 1
Figure 1. Fermion-bubble diagrams generating the Einstein–Cartan term. Left: a mixed [PITH_FULL_IMAGE:figures/full_fig_p015_1.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

39 extracted references · 4 linked inside Pith

  1. [26]

    Chkareuli, Nucl

    J.L. Chkareuli, Nucl. Phys. B941(2019) 425, arXiv:1901.07428 [hep-ph]; ibid B1020 (2025) 117150, arXiv: 2411.11854 [hep-th]

    arXiv 2019

  2. [1]

    Utiyama, Phys

    R. Utiyama, Phys. Rev.101(1956) 1597

    1956

  3. [2]

    Kibble, J

    T.W. Kibble, J. Math. Phys.2(1960) 212

    1960

  4. [3]

    Isham, A

    C.J. Isham, A. Salam and J. Strathdee, Lett. Nuovo Cim.5(1972) 969

    1972

  5. [4]

    Isham, A

    C.J. Isham, A. Salam and J. Strathdee, Phys. Rev. D8(1973) 2600, Phys. Rev. D9 (1974) 1702

    1973

  6. [5]

    Y.M. Cho, J. Math. Phys.16(1975) 2029, Phys. Rev. D14(1976) 3335; Y.M. Cho and P.G.O. Freund, Phys. Rev. D12(1975) 1711

    1975

  7. [6]

    Huang and P.W

    J.C. Huang and P.W. Dennis, Phys. Rev. D15(1977) 983, D24(1981) 3125

    1977

  8. [7]

    Percacci, Phys

    R. Percacci, Phys. Lett. B144(1984) 37, Nucl. Phys. B353(1991) 271; F. Nesti and R. Percacci, J. Phys. A41(2008) 075405, Phys. Rev. D81(2010) 025010

    1984

Show all 39 references
  1. [8]

    Chamseddine, Phys

    A.H. Chamseddine, Phys. Rev. D70(2004) 084006, Int. J. Geom. Meth. Mod. Phys. 3(2006) 149

    2004

  2. [9]

    Mankoc Borstnik, Nucl

    N.S. Mankoc Borstnik, Nucl. Phys. B994(2023) 116326

    2023

  3. [10]

    Chkareuli, Phys

    J.L. Chkareuli, Phys. Lett. B834(2022) 137417; Eur. Phys. J. C84(2024) 11, 1212, arXiv: 2310.11847 [hep-th]; Nucl. Phys. B1020(2025) 117150, arXiv: 2411.11854 [hep-th]

    2022 arXiv

  4. [11]

    Coleman and J

    S. Coleman and J. Mandula, Phys. Rev.159(1967) 1251

    1967

  5. [12]

    Neville, Phys.Rev

    D.E. Neville, Phys.Rev. D18(1978) 3535

    1978

  6. [13]

    Sezgin and P

    E. Sezgin and P. van Nieuwenhuizen, Phys. Rev. D21(1980) 3269

    1980

  7. [14]

    F.W. Hehl, P. von der Heyde, G.D. Kerlick and J.M. Nester, Rev. Mod. Phys. 48 (1976) 393

    1976

  8. [15]

    Navas et al

    S. Navas et al. (Particle Data Group), Phys. Rev. D110(2024) 3, 030001

    2024

  9. [16]

    Coleman and E

    S. Coleman and E. Weinberg, Phys. Review D 7 (1973)

    1973

  10. [17]

    Sakharov, Sov

    A.D. Sakharov, Sov. Phys. Dokl. 12 (1968) 1040

    1968

  11. [18]

    Adler, Rev

    S.L. Adler, Rev. Mod. Phys. 54 (1982) 729

    1982

  12. [19]

    Zee, Phys

    A. Zee, Phys. Rev. D 23 (1981) 858

    1981

  13. [20]

    Donoghue, Phys

    J.F. Donoghue, Phys. Rev. D50(1994) 3874

    1994

  14. [21]

    Georgi and S.L

    H. Georgi and S.L. Glashow, Phys. Rev. Lett.32(1974) 438

    1974

  15. [22]

    Dimopoulos and H

    S. Dimopoulos and H. Georgi, Nucl. Phys. B193(1981)150

    1981

  16. [23]

    Hisano, H

    J. Hisano, H. Murayama, T. Yanagida, Nucl. Phys. B402(1993) 46

    1993

  17. [24]

    Chkareuli, I.G

    J.L. Chkareuli, I.G. Gogoladze, Phys. Rev. D58(1998) 055011, arXiv: hep- ph/9803335 [hep-ph]

    1998

  18. [25]

    Georgi, Nucl

    H. Georgi, Nucl. Phys. B156(1979) 126

    1979

  19. [27]

    ’t Hooft, inRecent Developments in Gauge Theories, edited by G.’t Hooft et al (Plenum, New-York, 1980)

    G. ’t Hooft, inRecent Developments in Gauge Theories, edited by G.’t Hooft et al (Plenum, New-York, 1980)

    1980

  20. [28]

    J. L. Chkareuli, JETP Lett.32(1980) 671; Z. G. Berezhiani and J. L. Chkareuli, Sov. J. Nucl. Phys.37(1983) 618; J. L. Chkareuli, C. D. Froggatt and H. B. Nielsen, Nucl. Phys. B626(2002) 307, arXiv: hep-ph/0109156

    1980 arXiv

  21. [29]

    Mohapatra,Unification and Supersymmetry(Springer-Verlag, New-York, 2003)

    R.N. Mohapatra,Unification and Supersymmetry(Springer-Verlag, New-York, 2003)

    2003

  22. [30]

    Antoniadis, N

    I. Antoniadis, N. Arkani-Hamed, S. Dimopoulos and G. Dvali, Phys. Lett. B436 (1998) 257

    1998

  23. [31]

    Randall and R

    L. Randall and R. Sundrum, Phys. Rev. Lett.83(1999) 3370

    1999

  24. [32]

    Krasnov and Percacci, Class

    K. Krasnov and Percacci, Class. Quant. Grav.35(2018) 143001

    2018

  25. [33]

    Becker, M

    K. Becker, M. Becker, J.H. Schwarz,String Theory and M-Theory: A Modern Intro- duction(Cambridge Univ. Press, 2007)

    2007

  26. [34]

    Bjorken, Ann

    J.D. Bjorken, Ann. Phys. (N.Y.)24(1963) 174. 25

    1963

  27. [35]

    Phillips, Phys

    P.R. Phillips, Phys. Rev.146(1966) 966

    1966

  28. [36]

    Eguchi, Phys.Rev

    T. Eguchi, Phys.Rev. D14(1976) 2755

    1976

  29. [37]

    Terazava, Y

    H. Terazava, Y. Chikashige, K. Akama, Phys. Rev. D15(1977) 480

    1977

  30. [38]

    Suzuki, Phys

    M. Suzuki, Phys. Rev. D37(1988) 210; Phys. Rev. D82(2010) 045026

    1988

  31. [39]

    Chkareuli, Phys

    J.L. Chkareuli, Phys. Lett. B817(2021) 136281, arXiv: 2102.11217 [hep-ph]. 26

    2021 arXiv

Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.