Standard model with compactified spatial dimensions

Bartosz Fornal; Mark B. Wise

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Standard model with compactified spatial dimensions

Bartosz Fornal, Mark B. Wise

High Energy Physics - Theory · Submitted 5 Jun 2011

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We find that there are no stable one-dimensional vacua at zero temperature, although there does exist an unstable vacuum for a particular set of Dirac neutrino masses.

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The paper's own sentences, arranged. 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.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,249 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.69 · human participants 0.02 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.16 · compares with prior results 0.06 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We analyze the structure of the standard model coupled to gravity with spatial dimensions compactified on a three-torus. We find that there are no stable one-dimensional vacua at zero temperature, although there does exist an unstable vacuum for a particular set of Dirac neutrino masses.

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 analyze the structure of the standard model coupled to gravity with spatial dimensions compactified on a three-torus.	contribution 0.96	0.80	0.05	asserted 0.63
s1	We find that there are no stable one-dimensional vacua at zero temperature, although there does exist an unstable vacuum for a particular set of Dirac neutrino masses.	result 1.00	0.95	0.77	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.95.

What was examined, and what was not

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arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
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P abstract

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S sections
T body sentences
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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

The paper

Original abstract

We analyze the structure of the standard model coupled to gravity with spatial dimensions compactified on a three-torus. We find that there are no stable one-dimensional vacua at zero temperature, although there does exist an unstable vacuum for a particular set of Dirac neutrino masses.

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References

Forward citations

Cited by 5 Pith papers

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

Gauge Field Fluctuations Protect the Higgs Vacuum When a Small Universe Begins
hep-ph 2026-10 accept novelty 7.0 of 10

Gauge zero-mode fluctuations stabilize the Higgs vacuum in a small periodic box, yielding a testable lower bound on the top quark mass for the survival of the electroweak vacuum.
A Casimir turning point as the beginning of a small flat universe
gr-qc 2026-10 accept novelty 7.0 of 10

A flat three-torus universe can begin from a Casimir turning point, with the Higgs zero mode stabilized by gauge zero-point fluctuations, implying a testable top-mass bound and a fossil shape in the CMB.
Weak Gravity Conjecture, Multiple Point Principle and the Standard Model Landscape
hep-th 2017-07 conditional novelty 6.0 of 10

Compactifying the Standard Model on S^1 and T^2 produces lower-dimensional vacua whose flatness, under the multiple point principle, predicts Dirac neutrinos with the lightest mass of order 1 to 10 meV.
Constraining Neutrino Masses, the Cosmological Constant and BSM Physics from the Weak Gravity Conjecture
hep-th 2017-06 conditional novelty 6.0 of 10

Assuming stable anti-de Sitter vacua are forbidden in quantum gravity, the observed cosmological constant bounds neutrino masses below a few milli-electronvolts and caps the electroweak scale at 10^2 to 10^4 GeV.
Constraining the EW Hierarchy from the Weak Gravity Conjecture
hep-th 2017-07 conditional novelty 3.0 of 10

For a fixed cosmological constant and lightest-neutrino Yukawa coupling, the Weak Gravity Conjecture bounds the electroweak scale above at roughly 10^2 to 10^4 GeV, recasting the hierarchy problem as a swampland constraint.

How the literature uses it

7 arXiv papers cite this in 13 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

What it cites · 14 sentences without a confident label

Builds on 3 papers

This work completes the series of papers [ref] concerning lower-dimensional standard model vacua by considering the last remaining case, when all spatial dimensions are compactified.

Standard Model Vacua for Two-dimensional Compactifications · Introduction · 1.00
This work completes the series of papers [ref] concerning lower-dimensional standard model vacua by considering the last remaining case, when all spatial dimensions are compactified.

Finite Temperature Structure of the Compactified Standard Model · Introduction · 1.00
This work completes the series of papers [ref] concerning lower-dimensional standard model vacua by considering the last remaining case, when all spatial dimensions are compactified.

Quantum Horizons of the Standard Model Landscape · Introduction · 1.00

Uses the method or tool of 2 papers

We adopt the same parametrization as in [ref] ,

Quantum Horizons of the Standard Model Landscape · Compactification on a 3-torus at zero temperature · 0.97
In order to calculate the first term in ([ref]) we use the result of [ref] and, under the assumptions $Δ_11, (Δ̂) > 0$, write the sum over $n_2$ and $n_3$ as, ∑_n_2, n_3=-∞^∞' [d(n_2, n_3) +q]^-s+1/2 = 2 Δ_11^-s+1/2ζ_EH(s-12, qΔ_11) + 2 √(π) Γ(s-1)/Γ(s-1/2) Δ_11^s-3/2/D^s-1 ζ_EH(s-1, Δ_11 qD) + 8 π^s-1/2/Γ(s-1/2)1/√(Δ_11)∑_n_2, n_3=1^∞ n_2^s-1 ( D n_3^2 +Δ_11 q)^-s/2+1/2 ×cos(2π n_2 n_3 Δ_12Δ_11)K_s-1(2 π n_2Δ_11√(D n_3^2 + Δ_11 q)) where $D = (Δ̂)$ and the regularized form of the Epstein-Hurwitz zeta function is, ζ_EH(s, q) ≡ ∑_n=1^∞(n^2+q)^-s = -12q^-s + √(π)/2Γ(s-1/2)/Γ(s)q^-s+1/2 + 2 π^s/Γ(s)q^1-2s/4∑_n=1^∞n^s-1/2K_s-1/2(2πn √(q)) .

Standard Model Vacua for Two-dimensional Compactifications · Generalized multidimensional Chowla-Selberg formula · 0.90

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