Effective Actions for Strongly Interacting Fermionic Systems

Joerg Jaeckel

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Effective Actions for Strongly Interacting Fermionic Systems

Joerg Jaeckel

High Energy Physics - Phenomenology · Submitted 9 Sep 2003

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

The authors' main claim We find a first order chiral phase transition but no stable phase with broken color symmetry.

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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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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.65 · human participants 0.01 · controlled comparison 0.08 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.77 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We compare different non-perturbative methods for calculating the effective action for fermionic systems featuring bosonic bound states (BBS) and spontaneous symmetry breaking (SSB). In a purely fermionic language proceeding into the SSB phase requires techniques beyond perturbation theory and renormalization group equations. Improvement comes from a description with BBS fields and elementary fields treated on equal footing. Yet, ``partial bosonization'' introduces an arbitrariness as the choice for the composite fields is usually not completely determined by the classical action. Results of approximate calculations, e.g. mean field theory, may depend strongly on this choice, thus limiting their quantitative reliability. Using the Nambu--Jona-Lasinio model as an example we demonstrate how this dependence can be reduced, sometimes even be eliminated by suitably chosen approximations. Schwinger-Dyson equations (SDE) allow for a description of SSB without auxiliary fields. The 2PI effective action enables us to compare different solutions of the SDE and find the stable one. We apply this method to a six-fermion interaction resembling the three-flavor instanton interaction in QCD. We find a first order chiral phase transition but no stable phase with broken color symmetry. The existence of an elementary scalar boson in the Standard Model -- the Higgs -- raises several questions. The smallness of its mass compared to some fundamental scale ($\sim M_{\textrm{GUT}}$) requires an extreme amount of fine-tuning. Moreover, its $\phi^4$-potential may not be renormalizable in a strict sense. In view of this we discuss the possibility of a Higgs as BBS of fermions.

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 compare different non-perturbative methods for calculating the effective action for fermionic systems featuring bosonic bound states (BBS) and spontaneous symmetry breaking (SSB).	contribution 0.98	0.89	0.06	asserted 0.91
s1	In a purely fermionic language proceeding into the SSB phase requires techniques beyond perturbation theory and renormalization group equations.	background 0.88	0.10	0.05	asserted 1.00
s2	Improvement comes from a description with BBS fields and elementary fields treated on equal footing.	background 0.43	0.16	0.17	asserted 0.98
s3	Yet, ``partial bosonization'' introduces an arbitrariness as the choice for the composite fields is usually not completely determined by the classical action.	limitation 0.48	0.08	0.04	asserted 0.96
s4	Results of approximate calculations, e.g. mean field theory, may depend strongly on this choice, thus limiting their quantitative reliability.	background 0.60	0.10	0.04	hedged possibility 0.99
s5	Using the Nambu--Jona-Lasinio model as an example we demonstrate how this dependence can be reduced, sometimes even be eliminated by suitably chosen approximations.	contribution 0.73	0.87	0.16	asserted 0.90
s6	Schwinger-Dyson equations (SDE) allow for a description of SSB without auxiliary fields.	method 0.85	0.11	0.05	asserted 0.99
s7	The 2PI effective action enables us to compare different solutions of the SDE and find the stable one.	method 0.96	0.32	0.06	asserted 0.99
s8	We apply this method to a six-fermion interaction resembling the three-flavor instanton interaction in QCD.	method 0.75	0.91	0.04	asserted 1.00
s9	We find a first order chiral phase transition but no stable phase with broken color symmetry.	result 1.00	0.96	0.37	asserted 1.00
s10	The existence of an elementary scalar boson in the Standard Model -- the Higgs -- raises several questions.	background 1.00	0.06	0.02	asserted 0.95
s11	The smallness of its mass compared to some fundamental scale ($\sim M_{\textrm{GUT}}$) requires an extreme amount of fine-tuning.	background 1.00	0.05	0.02	asserted 0.99
s12	Moreover, its $\phi^4$-potential may not be renormalizable in a strict sense.	background 1.00	0.05	0.02	hedged possibility 0.97
s13	In view of this we discuss the possibility of a Higgs as BBS of fermions.	contribution 0.53	0.42	0.04	hedged possibility 0.84

What kind of paper the classifier reports this is: theoretical result 0.54 · evidence from simulation or computation 0.66.

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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 compare different non-perturbative methods for calculating the effective action for fermionic systems featuring bosonic bound states (BBS) and spontaneous symmetry breaking (SSB). In a purely fermionic language proceeding into the SSB phase requires techniques beyond perturbation theory and renormalization group equations. Improvement comes from a description with BBS fields and elementary fields treated on equal footing. Yet, ``partial bosonization'' introduces an arbitrariness as the choice for the composite fields is usually not completely determined by the classical action. Results of approximate calculations, e.g. mean field theory, may depend strongly on this choice, thus limiting their quantitative reliability. Using the Nambu--Jona-Lasinio model as an example we demonstrate how this dependence can be reduced, sometimes even be eliminated by suitably chosen approximations. Schwinger-Dyson equations (SDE) allow for a description of SSB without auxiliary fields. The 2PI effective action enables us to compare different solutions of the SDE and find the stable one. We apply this method to a six-fermion interaction resembling the three-flavor instanton interaction in QCD. We find a first order chiral phase transition but no stable phase with broken color symmetry. The existence of an elementary scalar boson in the Standard Model -- the Higgs -- raises several questions. The smallness of its mass compared to some fundamental scale ($\sim M_{\textrm{GUT}}$) requires an extreme amount of fine-tuning. Moreover, its $\phi^4$-potential may not be renormalizable in a strict sense. In view of this we discuss the possibility of a Higgs as BBS of fermions.

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References

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Cited by 7 Pith papers

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Within a functional renormalization group truncation of two-flavor QCD, vector mesons decouple from the physical spectrum above the pseudocritical scale and satisfy vector meson dominance to about 16 percent.
The QCD Phase Boundary from Quark-Gluon Dynamics
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Functional RG flow from the Z mass scale to the chiral regime gives a curvature of the one-flavor QCD phase boundary between 0.4 and 1.3, with the spread set by the choice of running coupling.
Chiral phase structure of QCD with many flavors
hep-ph 2005-07 conditional novelty 6.0 of 10

The chiral phase transition of many-flavor QCD occurs at Nf = 10.0 (+1.55/-0.63) for SU(3), computed from functional RG flow equations with all pointlike four-fermion channels included.

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Asymptotic safety: a simple example
hep-th 2010-11 accept novelty 4.0 of 10

The Gross-Neveu model in 2<d<4 is asymptotically safe at a non-Gaussian fixed point in both fermionic and partially bosonized functional-RG formulations, with critical exponents computed analytically at large Nf and n...
Fermion Interactions and Universal Behavior in Strongly Interacting Theories
hep-ph 2011-08 accept novelty 3.0 of 10

A pedagogical review argues that Wilsonian renormalization group flows of fermion interactions provide a common fixed-point and scaling language for QCD-like gauge theories, ultracold Fermi gases, and low-energy models.

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