Dynamical symmetry breaking in curved spacetime -review-

S. D. Odintsov; T. Inagaki; T. Muta

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Dynamical symmetry breaking in curved spacetime -review-

T. Inagaki, T. Muta, S. D. Odintsov

High Energy Physics - Theory · Submitted 12 Nov 1997

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

The authors' main claim It is also argued that the chiral symmetry broken by a weak magnetic field may be restored due to the presence of gravitational field.

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The compiled record

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, 4,944 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.16 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.16 · compares with prior results 0.10 · 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.

Four-fermion interaction models are considered to be prototype models for dynamical symmetry breaking.The present review deals with recent developments in the studies of dynamical symmetry breaking in the four-fermion interaction models and their extension in curved spacetime. Starting with the Minkowski spacetime in dimension $D$ ($2 \leq D \leq 4$) the effective potential in the leading order of $1/N$-expansion is calculated and the phase structure of the theory is investigated. In curved spacetime curvature-induced phase transitions are discussed in the circumstances where fermion masses are dynamically generated. Subsequently a possibility of curvature- and temperature-induced or curvature- and topology-induced phase transitions is discussed. It is also argued that the chiral symmetry broken by a weak magnetic field may be restored due to the presence of gravitational field. Finally some applications of four-fermion models in quantum gravity are briefly described.

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	Four-fermion interaction models are considered to be prototype models for dynamical symmetry breaking.The present review deals with recent developments in the studies of dynamical symmetry breaking in the four-fermion interaction models and their extension in curved spacetime.	background 0.67	0.23	0.08	asserted 0.99
s1	Starting with the Minkowski spacetime in dimension $D$ ($2 \leq D \leq 4$) the effective potential in the leading order of $1/N$-expansion is calculated and the phase structure of the theory is investigated.	method 0.73	0.58	0.05	asserted 0.99
s2	In curved spacetime curvature-induced phase transitions are discussed in the circumstances where fermion masses are dynamically generated.	contribution 0.93	0.29	0.11	asserted 0.87
s3	Subsequently a possibility of curvature- and temperature-induced or curvature- and topology-induced phase transitions is discussed.	contribution 0.97	0.38	0.07	hedged possibility 0.89
s4	It is also argued that the chiral symmetry broken by a weak magnetic field may be restored due to the presence of gravitational field.	result 0.76	0.37	0.18	hedged possibility 1.00
s5	Finally some applications of four-fermion models in quantum gravity are briefly described.	contribution 0.89	0.25	0.06	asserted 0.85

What kind of paper the classifier reports this is: review 1.00 · evidence from literature 0.69.

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

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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

The paper

Original abstract

Four-fermion interaction models are considered to be prototype models for dynamical symmetry breaking.The present review deals with recent developments in the studies of dynamical symmetry breaking in the four-fermion interaction models and their extension in curved spacetime. Starting with the Minkowski spacetime in dimension $D$ ($2 \leq D \leq 4$) the effective potential in the leading order of $1/N$-expansion is calculated and the phase structure of the theory is investigated. In curved spacetime curvature-induced phase transitions are discussed in the circumstances where fermion masses are dynamically generated. Subsequently a possibility of curvature- and temperature-induced or curvature- and topology-induced phase transitions is discussed. It is also argued that the chiral symmetry broken by a weak magnetic field may be restored due to the presence of gravitational field. Finally some applications of four-fermion models in quantum gravity are briefly described.

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References

Forward citations

Cited by 7 Pith papers

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

Leading Log Solution for Inflationary Yukawa
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Neutron star in Logarithmic model of Cartan $F(R)$ gravity
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In Cartan F(R) gravity with a logarithmic potential, a scalar field can raise the minimum neutron star mass to near one solar mass, but only for hand-tuned parameters that imply a huge vacuum energy.
Supersymmetric Nambu$-$Jona-Lasinio Model on ${\cal N}=1/2$ four-dimensional Non(anti)commutative Superspace
hep-th 2006-03 conditional novelty 6.0 of 10

On the N=1/2 deformed supersymmetric Nambu-Jona-Lasinio model, the one-loop effective potential has no nontrivial minimum, so no dynamical mass is generated.
Heat Kernel Methods for Multiloop Calculations in Curved Spacetime: Nonzero Spin
hep-th 2025-06 reject novelty 5.0 of 10

This paper presents a master formula and the off-diagonal heat kernel expansion (eq. 4.10) that generalize the authors' scalar curved-spacetime multiloop formalism to nonzero-spin fields in general gauge and gravitati...

Show 2 more citing papers

Chiral symmetry and curvature bounds in de Sitter spacetime
hep-th 2026-07 reject novelty 4.0 of 10

In the NJL model on de Sitter with an exponential proper-time cutoff, requiring a real constituent fermion mass imposes Λ_cosmo ≤ 6Λ_UV²/e².
Asymptotic safety of gravity with matter
hep-th 2022-12 conditional novelty 2.0 of 10

Asymptotically safe gravity may UV-complete the Standard Model and predict some of its couplings, but the evidence rests on truncated functional renormalization group calculations.

How the literature uses it

17 arXiv papers cite this in 27 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 whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper

We show that the gravitational field may compensate the effect of the magnetic field what leads to restoration of chiral symmetry.

Nambu-Jona-Lasinio Model in Curved Spacetime with Magnetic Field · 0.96

Papers citing it · 17 sentences without a confident label

Uses its method or tool 2 papers

Performing the path integrals of the fermion field, we obtain the effective potential in the leading order of the $1/N$ expansion [ref] , [equation] where $M$ is an arbitrary mass scale and the trace, $$, denotes the sum over the spinor indices.

Precise Phase Structure in Four-fermion Interaction Model on Torus · Four-fermion interaction model on torus · 0.91
Integrating out of the fermion with the cut-off regularization, we obtain the one-loop corrected potential [ref] , [equation]

Neutron star in Logarithmic model of Cartan $F(R)$ gravity · Effective potential of scalaron · 0.82

Compares with it 1 paper

The derived expressions for the effective potential reduce to the known results in the previous works at the periodic ($δ=0$) and anti-periodic ($δ=1$) boundary conditions [ref] .

Four-Fermion Interaction Model on $\mathcal{M}^{D-1} \otimes S^1$ · Conclusions · 0.98

Cites it as background 6 papers

The phenomenon is known to occur generically in fermionic systems of any dimension for various negatively curved spacetimes even at the weakest fermionic attraction [ref] .

A curvature bound from gravitational catalysis · Introduction · 0.87
It is known that the broken chiral symmetry is restored by the finite size effect for the anti-periodic boundary condition, $δ=1$ and the finite size effect enhances the chiral symmetry breaking for the periodic boundary condition, $δ=0$ [ref] .

Four-Fermion Interaction Model on $\mathcal{M}^{D-1} \otimes S^1$ · Four-fermion interaction model on $ℳ^D-1 ⊗S^1$ · 0.89
One could also employ other external probes like the electric field $E$ [ref] , the isospin chemical potential $μ_iso$ [ref] , the scalar curvature $R$ [ref] , the rotational angular velocity $ω$ [ref] , and their mixtures [ref] .

Perturbative confinement in thermal Yang-Mills theories induced by imaginary angular velocity · Introduction · 0.90

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