Dilaton and Chiral-Symmetry Breaking

Bardeen, William A.; Leung, Chung Ngoc; Love, S.T.

doi:10.1103/physrevlett.56.1230

Cited by 310 publications

(269 citation statements)

References 22 publications

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“…However, finiteness of the dynamically generated mass for Λ → ∞ forces non perturbative QED to be consistently defined only for those values of α and λ which lie on the critical surface. This is a simple corollary of the argument laid out in [6]. Note that as we employ a model for the vacuum polarization, the running coupling is not our prediction.…”

Section: Numerical Resultsmentioning

confidence: 74%

Vacuum polarization and dynamical chiral symmetry breaking: Phase diagram of QED with four-fermion contact interaction

et al. 2013

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We study chiral symmetry breaking for fundamental charged fermions coupled electromagnetically to photons with the inclusion of four-fermion contact self-interaction term, characterized by coupling strengths α and λ, respectively. We employ multiplicatively renormalizable models for the photon dressing function and the electron-photon vertex which minimally ensures mass anomalous dimension γm = 1. Vacuum polarization screens the interaction strength. Consequently, the pattern of dynamical mass generation for fermions is characterized by a critical number of massless fermion flavors N f = N c f above which chiral symmetry is restored. This effect is in diametrical opposition to the existence of criticality for the minimum interaction strengths, αc and λc, necessary to break chiral symmetry dynamically. The presence of virtual fermions dictates the nature of phase transition. Miransky scaling laws for the electromagnetic interaction strength α and the four-fermion coupling λ, observed for quenched QED, are replaced by a mean-field power law behavior corresponding to a second order phase transition. These results are derived analytically by employing the bifurcation analysis, and are later confirmed numerically by solving the original non-linearized gap equation. A three dimensional critical surface is drawn in the phase space of (α, λ, N f ) to clearly depict the interplay of their relative strengths to separate the two phases. We also compute the β-functions (βα and β λ ), and observe that αc and λc are their respective ultraviolet fixed points. The power law part of the momentum dependence, describing the mass function, implies γm = 1 + s, which reproduces the quenched limit trivially. We also comment on the continuum limit and the triviality of QED. 11.30.Rd, 11.15.Tk Since the works of Maskawa and Nakajima as well as the Kiev group [1], it is well known that quenched quantum electrodynamics (QED) exhibits vacuum rearrangement, which triggers chiral symmetry breaking when the interaction strength α = e 2 /(4π) exceeds a critical value α c ∼ 1. α c was argued to be an ultraviolet stable fixed point defining the continuum limit in supercritical QED. Although these works were carried out for the bare vertex in the Landau gauge, principle qualitative conclusions were later shown to be robust even for the most general and sophisticated ansätze put forward henceforth for an arbitrary value of the covariant gauge parameter, see e.g., [2][3][4][5]. Bardeen, Leung and Love [6] demonstrated that the composite operatorψψ acquires large anomalous dimensions at α = α c . In fact, the mass anomalous dimension was shown to be γ m = 1, leading to the fact that the four-fermion interaction operator (ψψ) 2 acquires the scaling dimension of d = 2(3 − γ m ) = 4 instead of 6, and becomes renormalizable. This is an example of when an interaction which is irrelevant in a certain region of phase space (perturbative) might become relevant in another (non perturbative). Consequently, the four-fermion contact interaction becomes mar...

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Section: Numerical Resultsmentioning

confidence: 74%

Vacuum polarization and dynamical chiral symmetry breaking: Phase diagram of QED with four-fermion contact interaction

et al. 2013

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“…A classic example is the Nambu-Jona-Lasinio model which was proposed some thirty years ago by Nambu and Jona-Lasinio [7] (see also [8]) as a quantum field theory which exhibits dynamical chiral symmetry breaking for sufficiently strong attractive fermionanti-fermion interactions in four (space-time) dimensions. The study of related models has recently seen a revival with speculations that the symmetry breaking mechanisms which it describes could be used in the standard model to describe the Higgs particle as a top quark condensate [9,10].…”

Section: Introductionmentioning

confidence: 99%

Four-Fermion Theory and the Conformal Bootstrap

Chen¹,

Makeenko²,

Semenoff³

1993

Annals of Physics

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We employ the conformal bootstrap to re-examine the problem of finding the critical behavior of four-Fermion theory at its strong coupling fixed point. Existence of a solution of the bootstrap equations indicates self-consistency of the assumption that, in space-time dimensions less than four, the renormalization group flow of the coupling constant of a four-Fermion interaction has a nontrivial fixed point which is generally out of the perturbative regime. We exploit the hypothesis of conformal invariance at this fixed point to reduce the set of the Schwinger-Dyson bootstrap equations for four-Fermion theory to three equations which determine the scale dimension of the Fermion field ψ, the scale dimension of the composite fieldψψ and the critical value of the Yukawa coupling constant. We solve the equations assuming this critical value to be small. We show that this solution recovers the fixed point for the four-fermion interaction with N -component fermions in the limit of large N at (Euclidean) dimensions d between two and four. We perform a detailed analysis of the 1/N -expansion in d = 3 and demonstrate full agreement with the conformal bootstrap. We argue that this is a useful starting point for more sophisticated computations of the critical indices.

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“…Eq. (14) is analogous to the gap equation in the continuum theory [5] containing gauge and four-fermion interactions. In fact, the infrared scale m = Σ c (0), i.e., the v.e.v.…”

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confidence: 99%

A possible origin of the Wilson lattice fermion

Preparata

Xue

1994

Physics Letters B

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Considering relevant and irrelevant high-dimension operators for ordinary and mirror fermions respectively, we show that the Wilson lattice fermion can originate from a spontaneous symmetry breaking phenomenon. Ward identities, due to symmetries at the cutoff, guarantee the cancellation of mirror-fermion contributions and the infrared limit can be achieved. The Wilson parameter turns out to be fixed at r ≃ 0.18, where the vacuum energy of the system is minimized.

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Dilaton and Chiral-Symmetry Breaking

Cited by 310 publications

References 22 publications

Vacuum polarization and dynamical chiral symmetry breaking: Phase diagram of QED with four-fermion contact interaction

Vacuum polarization and dynamical chiral symmetry breaking: Phase diagram of QED with four-fermion contact interaction

Four-Fermion Theory and the Conformal Bootstrap

A possible origin of the Wilson lattice fermion

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