The Hierarchy Problem and New Dimensions at a Millimeter

Gia Dvali; Nima Arkani-Hamed; Savas Dimopoulos

REVIEW

The Hierarchy Problem and New Dimensions at a Millimeter

Nima Arkani-Hamed, Savas Dimopoulos, Gia Dvali

High Energy Physics - Phenomenology · Submitted 11 Mar 1998 · 12 references

Pith's verdict: The founding large-extra-dimensions paper: a three-line derivation that makes the Planck scale derived rather than fundamental, with the localization mechanism openly postulated and one astrophysical bound the authors pass over too quickly.

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arXiv IDhep-ph/9803315 (version 1)

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CitationGia Dvali, Nima Arkani-Hamed, Savas Dimopoulos. "The Hierarchy Problem and New Dimensions at a Millimeter." arXiv:hep-ph/9803315 (1998). https://pith.science/paper/QO7UT5WP

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This is the paper that turned the hierarchy problem inside out: instead of raising the cutoff, it lowers the Planck scale to the weak scale and lets the observed 10^18 GeV fall out of geometry. Eq. 3, M_Pl^2 ~ M^(2+n) R^n with M ~ TeV, gives R ~ 0.1-1 mm for n=2. That number is the whole point. It is derived, not fitted, and it lands exactly where tabletop gravity experiments were about to look. The TeV-scale quantum gravity and the missing-energy / p_T-cutoff signatures follow from the same relation. The derivation is three lines of Gauss's law and it is right. Credit where due: the phenomenology section is honest about being order-of-magnitude (their words: 'we will very roughly estimate'), and the vortex model in Section 3 is explicitly labeled an existence proof, not a derivation. The authors also state their assumptions plainly: no dangerous higher-dimension operators (Section 1), a postulated bulk mass gap (Section 3.3), and the unaddressed origin of the millimeter scale (Section 4). Your classifier's 'limitations: none found' is wrong; they are all in the text. Two things to weigh. First, the localization postulate is load-bearing for the gauge sector, not for Eqs. 1-4. Section 3.3 says outright that they do not know how confinement works in a higher-dimensional theory. That is acceptable for the gravitational dilution claim and not acceptable for anyone who wants the full model to hang together. Second, and this one your reader underweighted: the paper's own SN 1987A estimate gives an effective F ~ 10^8 GeV for n=2, m_EW = 1 TeV, below the 10^10 GeV limit they themselves quote. The flagship scenario is therefore in tension with the paper's own astrophysical bound and needs n>2 or m_EW > 10 TeV. They mention it in passing; it deserves more than a passing mention. Who should read it: anyone working on the hierarchy, extra dimensions, or TeV-scale gravity, and anyone building sub-millimeter gravity experiments. It is the reference for the whole program. Recommendation: send it out. The central relation is correct and falsifiable, the soft spots are stated rather than hidden, and the follow-up literature needed a real referee report to anchor to.

Referee report

Significance

This is a genuinely new framework for the hierarchy problem, and its central relation is parameter-free: given m_EW and n, Eq. (4) fixes R with no adjustable constant, and the resulting numbers are falsifiable. The predictions are concrete and, importantly, testable in the near term: the n = 2 sub-millimeter deviation from Newtonian gravity is within reach of experiments the paper explicitly cites, and the TeV-scale quantum-gravity signatures at LHC/NLC are stated sharply enough to be confirmed or excluded. The paper is also commendably explicit about what is derived and what is postulated: Section 3 is framed as an 'existence proof' rather than a derivation, and the bulk mass-gap assumption of Section 3.3 is stated as a postulate. The construction of Section 3.4, while schematic, demonstrates that the localization requirement is not obviously impossible. The work opens a research direction and reframes the hierarchy problem in a way that has since proven influential.

Major objections (2)

[Section 3.3 and Section 3.4] The localization of the massless gauge fields rests on the postulate, stated plainly in Section 3.3, that 'the higher dimensional theory in the bulk will posses a mass gap ~ Lambda.' The four-dimensional toy model of Eq. (21) demonstrates the Dvali-Shifman mechanism in 4D, but the six-dimensional generalization is asserted rather than derived, and the three conditions listed at the end of Section 3.3 (nonabelian extension in the bulk, no light bulk matter, tree-level gauge coupling blowing up away from the vortex) are plausibility arguments, not a construction. The authors acknowledge this, and the central gravitational dilution relation of Eqs. (1)-(4) does not depend on it. What remains unresolved is the status of the framework's gauge sector: if the bulk does not confine, the photon delocalizes and the four-dimensional gauge coupling is not the observed one. I would ask the authors to state more sharply, in Section 3.3 or in the Summary, that the phenomenological viability of the localized-gauge-sector picture (as distinct from Eq. (4)) is conditional on this postulate, and to indicate what kind of calculation or lattice evidence would test it.
[Section 2 versus Abstract and Section 1] The paper's own supernova estimate in Section 2 gives an effective F ~ 10^8 GeV for n = 2 and m_EW = 1 TeV, below the quoted SN 1987A lower limit of 10^10 GeV, and the text correctly concludes that the constraint 'is easily satisfied if n > 2 or if m_EW > 10 TeV.' The authors acknowledge this tension. However, the Abstract and the Introduction present the n = 2, m_EW ~ TeV point as 'particularly exciting' and as the flagship scenario, without a forward reference to the SN 1987A caveat that appears only in Section 2. Since the abstract is the most-read part of the paper and the n = 2, TeV point is the one most likely to be quoted, I would ask for an explicit caveat or forward reference in the Abstract or at the end of Section 1, so that the flagship parameter point is not presented as unconstrained when the paper itself finds it in tension with its own astrophysical bound.

Minor objections (7)

[References] Reference [6] (Dixon, Harvey, Vafa, Witten) and reference [9] (Kim; Turner reviews) appear in the bibliography but do not appear to be cited anywhere in the body text. Either cite them at the appropriate places or remove them.
[Section 3.1, Eqs. (13)-(14)] The notation in Eq. (13) and Eq. (14) is hard to follow: the '+' superscript on the spinors is not defined, and the operator (-i Gamma^5 Gamma^6) uses the same labels 5 and 6 for both coordinate indices and gamma-matrix labels. A sentence defining the notation and distinguishing the two uses would help.
[Section 1, Eq. (1)] Eq. (1) omits the numerical coefficient of the (4+n)-dimensional gravitational potential. Since Eq. (4) is quoted as a quantitative result, it would be worth stating explicitly that the coefficient is O(1) and does not affect the estimate.
[Section 3.4] The soft hierarchy 'chi' ~ chi ~ Lambda ~ 10 H ~ m_EW is asserted without explanation of the factor of 10. A brief remark on its origin, or a statement that it is a schematic choice, would clarify whether this is a tuning or a convention.
[Section 1 and Abstract] The 'fireworks' picture of particles periodically returning to the 4D vacuum at frequency R^{-1} assumes that the escaping particle follows a closed geodesic on the compact manifold. For a generic torus with irrational ratios of velocity components the orbit is dense but not periodic, and return to the same 4D point requires special kinematics. The text hedges with 'for certain compact manifolds,' but a sentence spelling out this assumption would make the estimate of the return frequency more precise.
[Section 1 and Section 3.4] The sharp high-p_T cutoff at E_esc ~ m_EW assumes that the 4D manifold thickness is precisely m_EW^{-1}. Since the thickness is a model-dependent parameter, the cutoff energy is only as sharp as the localization width. The paper notes in Section 3.4 that naturalness requires migration not be postponed much beyond the TeV scale, but a sentence in Section 1 acknowledging that E_esc tracks the localization scale rather than being exactly m_EW would be appropriate.
[Acknowledgments and Section 2] There are several typographical errors: 'tuseful discussions' in the Acknowledgments, 'contructing' at the end of Section 2, 'posses' in Section 3.3, and 'longtitudinal' in Section 3.3. These should be corrected.

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The paper

The paper claims

The Planck scale may not be fundamental: if there are $n$ extra compact dimensions of radius $R$, Gauss's law in $4+n$ dimensions gives $M_{Pl}^2$ from a fundamental scale near 1 TeV, and for $n=2$ the crossover from $1/r^2$ to $1/r^4$ sits

The reading

The paper asks whether the gap between the weak scale and the Planck scale is a fact about nature or an artifact of assuming gravity is unmodified over thirty-three orders of magnitude in distance. Its answer is that the Planck scale need not be fundamental at all: with $n$ compact extra spatial dimensions of radius $R$, Gauss's law in $4+n$ dimensions gives $M_{Pl}^2$ from a fundamental scale near 1 TeV, and for $n=2$ the crossover from $1/r^2$ to $1/r^4$ gravity sits just below where Newtonian gravity has actually been tested. The prize is that the hierarchy problem dissolves rather than being stabilized: the cutoff of the theory is the weak scale, so there is no ultraviolet sensitivity left to explain, and no need for supersymmetry or technicolor.

What carries the argument

Two pieces of machinery carry the argument. The first is the matching condition $M_{Pl}^2

Extended reading notes

Core claim

The central claim is that $M_{Pl} = G_N^{-1/2}$ is a derived quantity, not a fundamental one. Take the only short-distance scale in nature to be $m_{EW}

Load-bearing premise

That Standard Model fields can really be pinned to a four-dimensional sheet only $1/m_{EW}$ thick while the graviton alone ranges over the bulk; the authors concede in Section 3.3 that they do not know how confinement works in a higher-dimensional theory and simply postulate the bulk mass gap, so the vortex model is offered as an existence proof rather than a derivation.

Original abstract

We propose a new framework for solving the hierarchy problem which does not rely on either supersymmetry or technicolor. In this framework, the gravitational and gauge interactions become united at the weak scale, which we take as the only fundamental short distance scale in nature. The observed weakness of gravity on distances $\gsim$ 1 mm is due to the existence of $n \geq 2$ new compact spatial dimensions large compared to the weak scale. The Planck scale $M_{Pl} \sim G_N^{-1/2}$ is not a fundamental scale; its enormity is simply a consequence of the large size of the new dimensions. While gravitons can freely propagate in the new dimensions, at sub-weak energies the Standard Model (SM) fields must be localized to a 4-dimensional manifold of weak scale "thickness" in the extra dimensions. This picture leads to a number of striking signals for accelerator and laboratory experiments. For the case of $n=2$ new dimensions, planned sub-millimeter measurements of gravity may observe the transition from $1/r^2 \to 1/r^4$ Newtonian gravitation. For any number of new dimensions, the LHC and NLC could observe strong quantum gravitational interactions. Furthermore, SM particles can be kicked off our 4 dimensional manifold into the new dimensions, carrying away energy, and leading to an abrupt decrease in events with high transverse momentum $p_T \gsim$ TeV. For certain compact manifolds, such particles will keep circling in the extra dimensions, periodically returning, colliding with and depositing energy to our four dimensional vacuum with frequencies of $ \sim 10^{12}$ Hz or larger. As a concrete illustration, we construct a model with SM fields localised on the 4-dimensional throat of a vortex in 6 dimensions, with a Pati-Salam gauge symmetry $SU(4) \times SU(2) \times SU(2)$ in the bulk.

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.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 8,490 input tokens, $0.0004 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.14 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.85 · compares with prior results 0.30 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We propose a new framework for solving the hierarchy problem which does not rely on either supersymmetry or technicolor. In this framework, the gravitational and gauge interactions become united at the weak scale, which we take as the only fundamental short distance scale in nature. The observed weakness of gravity on distances $\gsim$ 1 mm is due to the existence of $n \geq 2$ new compact spatial dimensions large compared to the weak scale. The Planck scale $M_{Pl} \sim G_N^{-1/2}$ is not a fundamental scale; its enormity is simply a consequence of the large size of the new dimensions. While gravitons can freely propagate in the new dimensions, at sub-weak energies the Standard Model (SM) fields must be localized to a 4-dimensional manifold of weak scale "thickness" in the extra dimensions. This picture leads to a number of striking signals for accelerator and laboratory experiments. For the case of $n=2$ new dimensions, planned sub-millimeter measurements of gravity may observe the transition from $1/r^2 \to 1/r^4$ Newtonian gravitation. For any number of new dimensions, the LHC and NLC could observe strong quantum gravitational interactions. Furthermore, SM particles can be kicked off our 4 dimensional manifold into the new dimensions, carrying away energy, and leading to an abrupt decrease in events with high transverse momentum $p_T \gsim$ TeV. For certain compact manifolds, such particles will keep circling in the extra dimensions, periodically returning, colliding with and depositing energy to our four dimensional vacuum with frequencies of $ \sim 10^{12}$ Hz or larger. As a concrete illustration, we construct a model with SM fields localised on the 4-dimensional throat of a vortex in 6 dimensions, with a Pati-Salam gauge symmetry $SU(4) \times SU(2) \times SU(2)$ in the bulk.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We propose a new framework for solving the hierarchy problem which does not rely on either supersymmetry or technicolor.	contribution 1.00	0.79	0.35	asserted 0.67
s1	In this framework, the gravitational and gauge interactions become united at the weak scale, which we take as the only fundamental short distance scale in nature.	contribution 0.72	0.35	0.20	asserted 0.99
s2	The observed weakness of gravity on distances $\gsim$ 1 mm is due to the existence of $n \geq 2$ new compact spatial dimensions large compared to the weak scale.	contribution 0.70	0.30	0.38	asserted 1.00
s3	The Planck scale $M_{Pl} \sim G_N^{-1/2}$ is not a fundamental scale; its enormity is simply a consequence of the large size of the new dimensions.	interpretation 0.82	0.34	0.15	asserted 1.00
s4	While gravitons can freely propagate in the new dimensions, at sub-weak energies the Standard Model (SM) fields must be localized to a 4-dimensional manifold of weak scale "thickness" in the extra dimensions.	method 0.54	0.32	0.09	asserted 0.95
s5	This picture leads to a number of striking signals for accelerator and laboratory experiments.	interpretation 0.72	0.42	0.07	asserted 0.90
s6	For the case of $n=2$ new dimensions, planned sub-millimeter measurements of gravity may observe the transition from $1/r^2 \to 1/r^4$ Newtonian gravitation.	interpretation 0.50	0.17	0.07	hedged possibility 1.00
s7	For any number of new dimensions, the LHC and NLC could observe strong quantum gravitational interactions.	result 0.52	0.26	0.10	hedged possibility 0.99
s8	Furthermore, SM particles can be kicked off our 4 dimensional manifold into the new dimensions, carrying away energy, and leading to an abrupt decrease in events with high transverse momentum $p_T \gsim$ TeV.	result 0.56	0.43	0.07	hedged possibility 0.63
s9	For certain compact manifolds, such particles will keep circling in the extra dimensions, periodically returning, colliding with and depositing energy to our four dimensional vacuum with frequencies of $ \sim 10^{12}$ Hz or larger.	result 0.65	0.41	0.05	hedged possibility 0.64
s10	As a concrete illustration, we construct a model with SM fields localised on the 4-dimensional throat of a vortex in 6 dimensions, with a Pati-Salam gauge symmetry $SU(4) \times SU(2) \times SU(2)$ in the bulk.	contribution 0.54	0.91	0.06	asserted 0.98

What kind of paper the classifier reports this is: theoretical result 0.96 · evidence from argument 0.90.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

Works cited (12)

[1]

R.Jackiw and P.Rossi, Nucl. Phys. B190, (1981) 681

View on Pith 1981
[2]

R.Jackiw and C.Rebbi, Phys. Rev.D13 (1976) 3398; E.Wein berg, Phys.Rev. D24 (1981) 2669

View on Pith 1976
[3]

H.B. Nielsen, P. Olesen, Nucl.Phys.B61 (1973) 45

View on Pith 1973
[4]

E. Witten, Nucl.Phys.B249 (1985) 557

View on Pith 1985
[5]

G. Dvali and M. Shifman, Phys.Lett.B396 (1997) 64

View on Pith 1997
[6]

L. Dixon, J.A. Harvey, C. Vafa and E. Witten, Nucl.Phys.B 261 (1985) 678

View on Pith 1985
[7]

See, e.g., V.Rubakov and M.Shaposhnikov, Phys. Lett. 12 5B (1983) 136; G.Dvali and M.Shifman, Nucl.Phys.B504 (1997) 127

View on Pith 1983
[8]

See A.Barnaveli and O.Kancheli, Sov. J. Nucl. Phys. 51 (3 ), (1990)

View on Pith 1990
[9]

For a review see, e.g. J. E. Kim, Phys. Rep. 150, (1987) 1; M .S.Turner, Phys.Rep.197 (1990) 67-97

View on Pith 1987
[10]

J. Polchinski , “TASI Lectures on D-Branes”, hep-th/96 11050

View on Pith
[11]

J.C. Price, in proc. Int. Symp. on Experimental Gravita tional Physics, ed. P.F. Michelson, Guangzhou, China (World Scientiﬁc, Sin gapore 1988); J.C.Price et. al., NSF proposal 1996; A.Kapitulnik a nd T. Kenny, NSF proposal, 1997

View on Pith 1988
[12]

S.Dimopoulos and H.Georgi, Nucl. Phys. B193,(1981), 1 50. 16

View on Pith 1981

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Is the Lightest Kaluza-Klein Particle a Viable Dark Matter Candidate?
hep-ph 2002-06 accept novelty 7.0 of 10

In universal extra dimensions, the lightest Kaluza-Klein particle (a KK photon or KK neutrino at the TeV scale) can have the right annihilation rate to account for the observed dark matter density.
Classical Black Hole Production in High-Energy Collisions
gr-qc 2002-01 accept novelty 7.0 of 10

An explicit closed trapped surface is constructed for off-center collisions of two ultra-relativistic particles in four dimensions, giving a rigorous lower bound on the black hole production cross-section of about 65 ...
Largest temperature of the radiation era and its cosmological implications
hep-ph 2000-05 accept novelty 7.0 of 10

If the reheat temperature was as low as 0.7 MeV, WIMPs, neutrinos, and axions can be far heavier or more weakly coupled than standard cosmology allows, and the usual dark-matter mass bounds dissolve.
Grand Unification at Intermediate Mass Scales through Extra Dimensions
hep-ph 1998-06 conditional novelty 7.0 of 10

Extra spacetime dimensions make gauge couplings run as power laws, so they unify at intermediate or TeV scales instead of the usual 10^16 GeV.
Scattering of massless scalar waves by higher-dimensional regular black holes in general relativity coupled to nonlinear electrodynamics
gr-qc 2026-10 conditional novelty 6.0 of 10

Massless scalar scattering by D-dimensional Bardeen/Hayward regular black holes has a universal inverse-fourth-power forward divergence at fixed frequency, with the steeper classical law appearing only at larger angle...
Momentum-space entanglement and mutual information in Kaluza-Klein reduction
hep-th 2026-10 accept novelty 6.0 of 10

In a 5D scalar on a circle with a cubic interaction, the mutual information between the low-energy sector and one Kaluza-Klein level falls as 1/m_n, and its sum over levels grows logarithmically with the number of levels.
Relating Dark Dimension Size with Dark Energy via 5D Quintessence Potential and Casimir Energy
hep-th 2026-10 conditional novelty 6.0 of 10

A 5D model with induced gravity can relate the dark dimension size to dark energy, but requires a large number of species and a tuned hierarchy, while other models face insurmountable obstacles.
Relic of the Kink Shape Mode in a Topological Thick Brane - some implications
hep-th 2026-09 conditional novelty 6.0 of 10

The flat-space kink's shape mode survives in the gravitating thick brane as a narrow quasi-bound resonance, and for weak gravity it can dominate energy transfer to brane matter.
Localization of Vector and Fermion Fields on a Thick Brane with a Lump-type Scalar Background
gr-qc 2026-09 accept novelty 6.0 of 10

In a lump-type scalar braneworld, vector and fermion zero modes are localized via a direct coupling to the lump scalar, with both chiralities of fermions localizable simultaneously under a parameter condition.
Batalin-Vilkovisky description of Yang-Mills theories with universal extra dimensions
hep-th 2026-09 accept novelty 6.0 of 10

A Batalin-Vilkovisky description of pure Yang-Mills theories with universal extra dimensions is constructed, including a proper solution to the master equation and a manifestly covariant gauge-fixing procedure.
The Dark Dimension and Majorana Neutrinos
hep-ph 2026-09 conditional novelty 6.0 of 10

Terrestrial neutrino experiments constrain the Dark Dimension scenario, with KATRIN beta decay forcing Yukawa couplings to O(10^{-3}) in the favored parameter window.
Search for high-mass resonances in photon-jet final states using 140 fb$^{-1}$ of $pp$ collisions at $\sqrt{s} = 13$ TeV with the ATLAS detector
hep-ex 2026-08 accept novelty 6.0 of 10

No evidence for high-mass resonances in photon-jet events is observed; ATLAS sets 95% CL exclusion limits on excited quarks up to 6.0 TeV (q*_L), 3.5 TeV (c*), 2.6 TeV (b*) and on quantum black hole thresholds up to 5...
On the Origins of Varying Gauge Couplings
hep-ph 2026-08 accept novelty 6.0 of 10

In weakly coupled, renormalizable four-dimensional theories, gauge invariance forces the effective gauge coupling to depend on a singlet scalar VEV only logarithmically at leading order, not linearly.
TransPlanckian Censorship on Dark Dimension Inflation
hep-th 2026-07 conditional novelty 6.0 of 10

TransPlanckian Censorship forces dark-dimension inflation into a narrow one-dimension window with a pre-inflationary phase and suppresses tensor modes to r < 10^-10.
Searching for the $N$-naturalness tower of neutrinos
hep-ph 2026-07 conditional novelty 6.0 of 10

Neutrino data rule out the Majorana realization of N-naturalness with up to 10^4 sectors and fine-tuning r ≥ 0.1, including the no-fine-tuning GUT benchmark.
Quantization of Brane-Skyrmions via Physics-Informed Neural Networks
hep-th 2026-06 unverdicted novelty 6.0 of 10

Quantizes Brane-Skyrmions perturbatively in J² and employs PINNs to minimize energy while incorporating quantized spin backreaction for potential hadronic spectra modeling.
Thick branes and fermion localization in five-dimensional $f(T,T_G)$ gravity
hep-th 2026-05 unverdicted novelty 6.0 of 10

In 5D f(T, T_G) gravity, thick branes develop splitting and internal structure controlled by the coupling, while supporting a normalizable chiral fermion zero mode and modified resonant Kaluza-Klein states due to the ...
Polydoxon Transformations and Scientific Reward in Physics
physics.hist-ph 2026-05 unverdicted novelty 6.0 of 10

The paper develops a descriptive framework in which scientific reward in physics is understood as transformations of the Polydoxon, the structured set of viable theories, with reward scaling by the transformation's sc...
Micron-sized Extra Dimensions and Primordial Black Holes: Charged, Rotating, and Memory Burdened
hep-ph 2026-04 unverdicted novelty 6.0 of 10

Six-dimensional primordial black holes with memory burden effects can survive as light dark matter in a two-extra-dimension model at the 10 TeV scale, producing high-multiplicity thermal events at future colliders.
Gravitational Properties of the Monopole Bag
hep-ph 2026-04 unverdicted novelty 6.0 of 10

Monopole bags in axion models can collapse into horizonless objects or dyonic regular black holes that evade singularities and retain axionic structure through Chern-Simons effects.
Scattering of kinks in Frankensteinian potentials: Kinks as bubbles of exotic mass and phase transitions in oscillon production
hep-th 2026-03 unverdicted novelty 6.0 of 10

In two Frankensteinian potentials, kink scattering shows a phase-transition-like change from massive wave disintegration to oscillon production when field thresholds are low enough.
Axiverse Lampposts
hep-ph 2026-02 conditional novelty 6.0 of 10

In a hierarchical multi-axion theory with random couplings, axion field ranges shrink with 1/sqrt(N), generic axion–SM couplings are suppressed, but the QCD axion's coupling is unsuppressed.

See all 281 Pith citations

How later papers used it

1,029 later papers cite it

Evidence: substantial. 1,008 of the citing papers share no author with it, and 34 of those carry a confident label from Pith's citation classifier.

Pith read 39 of the 1,364 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

3 later papers by other authors are listed below: 1 built on it and 2 compared their own results with it.

Builds on it 1 of 3 papers with this label

Extended these constructions to include the case where two dimensions are on sub-micron scales.

Anisotropic Modulus Stabilisation: Strings at LHC Scales with Micron-sized Extra Dimensions (2011) · 1.00 · paraphrased: the licence does not allow quoting

Compares with it 2 of 30 papers with this label

Compared its signal with the ADD model, in which Kaluza-Klein graviton emission also shows up as the process e+e- to gamma plus, which may also occur at sizeable cross section.

Vector bosons escaping from the brane: $e^+e^- \to \gamma +$ nothing (2010) · 0.98 · paraphrased: the licence does not allow quoting
Compared the number of new degrees of freedom it introduces, which may seem outrageous, with that in models with large extra dimensions, finding it of the same order.

Quantum gravity at a TeV and the renormalization of Newton's constant (2008) · 0.96 · paraphrased: the licence does not allow quoting

How the literature uses it

950 arXiv papers cite this in 1,261 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 457 sentences without a confident label

Contests it 1 paper

In addition, a specific semiclassical approach [ref] , based on the GUP with the quadratic momentum term [ref] , makes an interesting attempt although it does not solve the cosmological constant problem even in models with large extra dimensions [ref] .

Interpretation of the Cosmological Constant Problem within the Framework of Generalized Uncertainty Principle · Introduction · contest 0.78

Builds on it 3 papers

In a previous work [ref] we extended an argument of Nieves and Pal [ref] to calculate the amplitude for the one-loop decay of a Z boson to a photon and a Kaluza-Klein graviton, in a form applicable to an effectively continuous spectrum of graviton excitations [ref] in the ADD model [ref] .

Production of a Z boson and a photon via a Randall-Sundrum-type graviton at the Large Hadron Collider · Introduction · 0.89
On the other hand, in paper [ref] unification of gravity with electroweak interactions at TeV-scale, as suggested in Refs. [ref] , was studied and the results obtained in [ref] could be extended up to the scale of the order about $10^12$ GeV.

Cosmic rays from heavy particle decays · Introduction · 0.81
The present work extends these constructions to include the most extreme and interesting case where two dimensions are on sub-micron scales [ref] .

Anisotropic Modulus Stabilisation: Strings at LHC Scales with Micron-sized Extra Dimensions · Conclusions · 1.00

Uses its data or values 1 paper

The minimum energy needed to form a black hole in a collider is given by [equation] In order to investigate the minimal energy for black hole formation, we use the latest observed limits on the ADD model [ref] parameter $M_p$ with a next-to-leading-order (NLO) $K$-factor [ref] .

Quantum corrections to the thermodynamics of Schwarzschild-Tangherlini black hole and the generalized uncertainty principle · Black hole remnants in the colliders · 0.84

Compares with it 29 papers

From the relation ([ref]), we get a similar result in [ref] .

Aspects of $(d+D)$-dimensional Anisotropic Conformal Gravity · Vacuum Solution · 0.96
We also make comparison with the ADD model [ref] in which the emission of a Kaluza–Klein graviton also shows up as the process $e^+e^- →γ+$, which may also occur at sizeable cross section [ref] .

Vector bosons escaping from the brane: $e^+e^- \to \gamma +$ nothing · Introduction · 0.98
In this way we get induced gravitational parameters on $Σ^q$ that are reminiscent of the Kaluza-Klein-type theories [ref] with the radius of curvature $ρ$ playing the role of the compactification radius[The localization of the energy near the submanifold $Σ^q$ in this model is over a cosmological distance.].

Emergent Gravity in Spaces of Constant Curvature · Introduction · 0.90

Cites it as support 1 paper

It turns out that extra dimensions can be large enough to allow $1/L ∼eV$ without running into conflict with observations [ref] and so can allow bulk supersymmetry to play a role suppressing the vacuum energy right down the the Dark Energy scale [ref] .

Dark Energy and the Symbiosis Between Micro-physics and Cosmology (Naturally) · The extra-dimensional loophole · 0.98

Cites it as background 655 papers

Historically, this deception has been attributed to (e.g.) the presence of a warped [ref] or large [ref] extra dimension, but more recently a new set of clockwork models [ref] have emerged, which show signs of promise.

Clockwork Cosmology · Introduction · 0.90
In models of LSG with large extra dimensions [ref] , graviton exchange ($r=2$)

Eikonal contributions to ultra high energy neutrino-nucleon cross sections in low scale gravity models · Theory · 0.97
Using the idea of large extra dimensions, Arkani-Hamed, Dimopoulos, and Dvali (ADD) suggested a phenomenological brane-world scenario for unifying the elementary particle forces with gravity near the electroweak energy scale [ref] .

Minimum length, extra dimensions, modified gravity and black hole remnants · Introduction · 0.96

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [1]

R.Jackiw and P.Rossi, Nucl. Phys. B190, (1981) 681

View on Pith 1981

[2] [2]

R.Jackiw and C.Rebbi, Phys. Rev.D13 (1976) 3398; E.Wein berg, Phys.Rev. D24 (1981) 2669

View on Pith 1976

[3] [3]

H.B. Nielsen, P. Olesen, Nucl.Phys.B61 (1973) 45

View on Pith 1973

[4] [4]

E. Witten, Nucl.Phys.B249 (1985) 557

View on Pith 1985

[5] [5]

G. Dvali and M. Shifman, Phys.Lett.B396 (1997) 64

View on Pith 1997

[6] [6]

L. Dixon, J.A. Harvey, C. Vafa and E. Witten, Nucl.Phys.B 261 (1985) 678

View on Pith 1985

[7] [7]

See, e.g., V.Rubakov and M.Shaposhnikov, Phys. Lett. 12 5B (1983) 136; G.Dvali and M.Shifman, Nucl.Phys.B504 (1997) 127

View on Pith 1983

[8] [8]

See A.Barnaveli and O.Kancheli, Sov. J. Nucl. Phys. 51 (3 ), (1990)

View on Pith 1990

[9] [9]

For a review see, e.g. J. E. Kim, Phys. Rep. 150, (1987) 1; M .S.Turner, Phys.Rep.197 (1990) 67-97

View on Pith 1987

[10] [10]

J. Polchinski , “TASI Lectures on D-Branes”, hep-th/96 11050

View on Pith

[11] [11]

J.C. Price, in proc. Int. Symp. on Experimental Gravita tional Physics, ed. P.F. Michelson, Guangzhou, China (World Scientiﬁc, Sin gapore 1988); J.C.Price et. al., NSF proposal 1996; A.Kapitulnik a nd T. Kenny, NSF proposal, 1997

View on Pith 1988

[12] [12]

S.Dimopoulos and H.Georgi, Nucl. Phys. B193,(1981), 1 50. 16

View on Pith 1981