Gauged Nambu Jona-Lasinio Model Research Articles

Ideal walking dynamics via a gauged NJL model

According to the Ideal Walking Technicolor paradigm large mass anomalous dimensions arise in gauged Nambu--Jona-Lasinio (NJL) models when the four-fermion coupling is sufficiently strong to induce spontaneous symmetry breaking in an otherwise conformal gauge theory. We therefore study the $SU(2)$ gauged NJL model with two adjoint fermions using lattice simulations. The model is in an infrared conformal phase at small NJL coupling while it displays a chirally broken phase at large NJL couplings. In the infrared conformal phase we find that the mass anomalous dimension varies with the NJL coupling reaching $\gamma_m \sim 1$ close to the chiral symmetry breaking transition, de facto making the present model the first explicit realization of the Ideal Walking scenario.

An alternative attractor in gauged NJL inflation

We have investigated the attractor structure for the CMB fluctuations in a composite inflation scenario within the gauged Nambu–Jona-Lasinio (NJL) model. Such composite inflation represents an attractor which cannot be found in a fundamental scalar model. As is known, the number of inflationary models contains the attractor classified by the α-attractor model. It is found that the attractor inflation in the gauged NJL model corresponds to the case.

Inflation from the finite scale gauged Nambu–Jona-Lasinio model

The possibility to construct an inflationary universe scenario for the finite-scale gauged Nambu–Jona-Lasinio model is investigated. This model can be described by the Higgs–Yukawa type interaction model with the corresponding compositeness scale. Therefore, the one-loop Higgs–Yukawa effective potential is used with the compositeness condition for the study of inflationary dynamics. We evaluate the fluctuations in the cosmic microwave background for the model with a finite compositeness scale in the slow-roll approximation. We find the remarkable dependence on the gauge group and the number of fermion flavors. It is also proved that the model has similar behavior with the ϕ4n chaotic inflation and the Starobinsky model at the flat and steep limits, respectively. It is demonstrated that realistic inflation consistent with Planck data is possible for a range of theory parameters.

Dynamical Symmetry Breaking in Curved Spacetime

This review deals with the theory of four-fermion interactions in curved spacetime. Starting with the D-dimensional Minkowski spacetime (2 ≤ D ≤ 4) the effective potential in the leading order of 1/N-expansion is calculated and the phase structure of the theory is investigated. Using the same technique the effective potential for composite operator ψψ in four-fermion models is calculated under the following circumstances: a) D-dimensional weakly curved spacetime (in linear curvature approximation), b) D-dimensional de Sitter and anti-de Sitter universe, c) D-dimensional Einstein universe. The phase structure of the theory is investigated analytically as well as numerically. Curvature induced phase transitions are discussed where fermion masses are dynamically generated. As an extension of four-fermion models we consider the gauged Nambu-Jona-Lasinio (NJL) model, higher derivative NJL model and supersymmetric NJL model in weakly curved spacetime where the effective potential is analytically evaluated. The phase structure of the models is again analyzed and the condition for the chiral symmetry breaking in the gauged NJL model is given in an analytical form. Finally the influence of two external effects (non-zero temperature and gravitational field, nontrivial topology and gravitational field as well as magnetic and gravitational field) to the phase structure of four-fermion models is analyzed. The possibility of curvature and temperature-induced or curvatureand 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. Some applications of four-fermion models in quantum gravity are also briefly investigated. This paper was published in Prog. Theor. Phys. Suppl. 127 (1997) 93. 1e-mail : inagaki@ipc.hiroshima-u.ac.jp 2e-mail:muta@sci.hiroshima-u.ac.jp 3e-mail:sergei@ecm.ub.es, odintsov@quantum.univalle.edu.co

PHASE DIAGRAM OF TWO-FLAVOR QUARK MATTER: GLUONIC PHASE AT NONZERO TEMPERATURE

The phase structure of neutral two-flavor quark matter at nonzero temperature is studied. Our analysis is performed within the framework of a gauged Nambu–Jona-Lasinio model and the mean-field approximation. We compute the free energy of the gluonic phase (gluonic cylindrical phase II) in a self-consistent manner and investigate the phase transition from the gluonic phase to the 2SC/g2SC/NQ phases. We briefly consider the phase diagram in the plane of coupling strength versus temperature and discuss the mixed phase consisting of the normal quark and 2SC phases.

Top mode standard model in six dimensions

We construct a top-mode standard model where the third generation fermions and the SU(2)_L \times U(1)_Y gauge bosons are put on a 6-dimensional brane(5-brane) with the extra dimensions compactified on the TeV scale(R_5^{-1}=R_6^{-1} \equiv R^{-1}= 1-10 TeV), while only the gluons live in a compactified 8-dimensional bulk(R_7^{-1}=R_8^{-1} \equiv \Lambda \gg R^{-1}).On the 5-brane, Kaluza-Klein (KK) modes of the bulk gluons give rise to induced four-fermion interactions which, combined with the gauge interactions, are shown to be strong enough to trigger the top quark condensate, based on the dynamics of 6-dimensional gauged Nambu-Jona-Lasinio (NJL) model. Moreover, we can use a freedom of the brane positions to tune the four-fermion coupling close to the critical line of 6-dimensional gauged NJL model, so that the gap equation can ensure the top condensate on the weak scale while keeping other fermions massless. There actually exists a scale (``tMAC scale''), \Lambda_{\rm tM} = (7.8-11.0) R^{-1}, where the running gauge couplings combined with the induced four-fermion interactions trigger only the top condensate while no bottom and tau condensates. Furthermore, presence of such explicit four-fermion interactions enables us to formulate straightforwardly the compositeness conditions at \Lambda=\Lambda_{\rm tM}, which, through the renormalization-group analysis, yields a prediction of masses of the top quark and the Higgs boson, m_t = 177 - 187 GeV and m_H = 183 - 207 GeV.

Gauged Nambu-Jona-Lasinio model with extra dimensions: Phase structure and renormalizability

We investigate phase structure of the D (> 4)-dimensional gauged Nambu-Jona-Lasinio (NJL) model with $\delta(=D-4)$ extra dimensions compactified on TeV scale, based on the improved ladder Schwinger-Dyson (SD) equation in the bulk. We assume that the bulk running gauge coupling in the SD equation for the SU(N_c) gauge theory with N_f massless flavors is given by the truncated Kaluza-Klein effective theory and hence has a nontrivial ultraviolet fixed point (UVFP). We find the critical line in the parameter space of two couplings, the gauge coupling and the four-fermion coupling, which is similar to that of the gauged NJL model with fixed (walking) gauge coupling in four dimensions. It is shown that in the presence of such walking gauge interactions the four-fermion interactions become ``nontrivial'' even in higher dimensions, similarly to the four-dimensional gauged NJL model. Such a nontriviality holds only in the restricted region of the critical line (``nontrivial window'') with the gauge coupling larger than a non-vanishing value (``marginal triviality (MT)'' point), in contrast to the four-dimensional case where such a nontriviality holds for all regions of the critical line except for the pure NJL point. In the nontrivial window the renormalized effective potential yields a nontrivial interaction which is conformal invariant. The exisitence of the nontrivial window implies ``cutoff insensitivity'' of the physics prediction in spite of the ultraviolet dominance of the dynamics. In the formal limit D -> 4, the nontrivial window coincides with the known condition of the nontriviality of the four-dimensional gauged NJL model, $9/(2N_c) < N_f - N_c < 9/2 N_c$.

Non-Perturbative Renormalization Group and Renormalizability of Gauged NJL Model

Non-perturbative renormalizability, or non-triviality, of the gauged Nambu-Jona-Lasinio (NJL) model in four dimensions is examined by using non-perturbative (exact) renormalization group in large $N_c$ limit. When running of the gauge coupling is asymptotically free and slow enough, the two dimensional renormalized trajectory (subspace) spanned by the four fermi coupling and the gauge coupling is found to exist, which implies renormalizability of the gauged NJL model. In the case of fixed gauge coupling, renormalizability of the model turns out to be guaranteed by the line of the UV fixed points. We discuss also non-triviality of the gauged NJL model extended to include higher dimensional operators and correspondence with the gauge-Higgs-Yukawa system.

Analytic structure of scalar composites in the symmetric phase of the gauged Nambu–Jona-Lasinio model

The gauged Nambu-Jona-Lasinio model in the quenched-ladder approximation has non-trivial dynamics near a critical scaling region (critical curve) separating a chiral symmetric and a dynamically chiral symmetry broken phase. Scalar and pseudoscalar composites corresponding to the four-fermion interaction become relevant degrees of freedom at short distances, which is reflected in the appearance of a large anomalous dimension of the four-fermion operators. A method is introduced for solving the Schwinger-Dyson equation for the Yukawa vertex in specific kinematic regimes. This allows one to derive an analytic expression for the scalar propagator, which is valid along the entire critical curve. The mass and width of the scalar composites in the critical scaling region are reexamined and the conformal phase transition at the critical gauge coupling is discussed.

Chiral symmetry breaking in the gauged NJL model in curved spacetime.

Using the renormalization group (RG) approach and the equivalency between the class of gauge-Higgs-Yukawa models and the gauged Nambu--Jona-Lasinio (NJL) model, we study the gauged NJL model in curved space-time. The behavior of the scalar-gravitational coupling constant \ensuremath{\xi}(t) in both theories is discussed. The RG-improved effective potential of the gauged NJL model in curved spacetime is found. The curvature at which chiral symmetry in the gauged NJL model is broken is obtained explicitly in a remarkably simple form. The powerful RG-improved effective potential formalism leads to the same results as ladder Schwinger-Dyson equations which have not been formulated yet in curved spacetime. \textcopyright{} 1996 The American Physical Society.

The continuum limit of non compact QED

Since four-fermion operators in strongly coupled QED are nonperturbatively renormalizable, we analyze here the phase diagram and critical behaviour of the Gauged Nambu-Jona Lasinio model. Our mean field approximation relates the critical exponents along the continuous phase transition line with the mass dependence of the chiral condensate in the Coulomb phase of standard noncompact QED . The numerical results for noncompact QED strongly suggest non mean field exponents along the critical line.

Nontriviality of Gauge-Higgs-Yukawa System and Renormalizability of Gauged Nambu–Jona-Lasinio Model

Nontriviality of Gauge-Higgs-Yukawa System and Renormalizability of Gauged Nambu–Jona-Lasinio Model

The gauged Nambu-Jona Lasinio model: a mean field calculation with nonmean field exponents

We analyse the phase diagram of the lattice gauged Nambu-Jona Lasinio model with the help of a mean field approximation plus numerical simulations. We find a phase transition line in the coupling parameters space separating the chirally broken phase from the symmetric phase, which is in good qualitative agreement with results obtained in the quenched-ladder approximation. The mean field approximation relates the critical exponents along the continuous phase transition line with the mass dependence of the chiral condensate in the Coulomb phase of standard noncompact QED. Our numerical results for noncompact QED strongly suggest nonmean field exponents along the critical line.

Nontriviality of Gauge-Higgs-Yukawa System and Renormalizability of Gauged NJL Model

In the leading order of a modified 1/NC expansion, we show that a class of gauge-Higgs-Yukawa systems in four dimensions give non-trivial and well-defined theories in the continuum limit. The renormalized Yukawa coupling y and the quartic scalar coupling λ have to lie on a certain line in the (y, λ) plane and the line terminates at an upper bound. The gauged Nambu-Jona-Lasinio (NJL) model in the limit of its ultraviolet cutoff going to infinity, is shown to become equivalent to the gauge-Higgs-Yukawa system with the coupling constants just on that terminating point. This proves the renormalizability of the gauged NJL model in four dimensions. The effective potential for the gauged NJL model is calculated by using renormalization group technique and confirmed to be consistent with the previous result by Kondo, Tanabashi and Yamawaki obtained by the ladder Schwinger-Dyson equation.

Nontriviality of Gauge-Higgs-Yukawa System and Renormalizability of Gauged NJL Model

In the leading order of a modified 1/Nc expansion, we show that a class of gauge-Higgs-Yukawa systems in four dimensions give non-trivial and well-defined theories in the continuum limit. The renormalized Yukawa coupling y and the quartic scalar coupling \lambda have to lie on a certain line in the (y,\lambda) plane and the line terminates at an upper bound. The gauged Nambu--Jona-Lasinio (NJL) model in the limit of its ultraviolet cutoff going to infinity, is shown to become equivalent to the gauge-Higgs-Yukawa system with the coupling constants just on that terminating point. This proves the renormalizability of the gauged NJL model in four dimensions. The effective potential for the gauged NJL model is calculated by using renormalization group technique and confirmed to be consistent with the previous result by Kondo, Tanabashi and Yamawaki obtained by the ladder Schwinger-Dyson equation.

The vacuum structure in a supersymmetric gauged Nambu—Jona-Lasinio model

The dynamical breakdown of the SU(2)XU(1) symmetry triggered by a top—antitop condensate is studied in a supersymmetric version of the gauged Nambu—Jona-Lasinio model. An effective potential approach is used to investigate the vacuum structure and the equivalence with the minimal supersymmetric standard model. The role of the soft supersymmetry breaking terms is analyzed in detail in a version of the model where the electroweak gauge interactions are turned off.

Critical behavior of the gauged Nambu-Jona-Lasinio model in 2+1 dimensions.

In this article we study the phase structure of the gauged [U(1)] Nambu--Jona-Lasinio model in 2+1 dimensions. We calculate the effective potential and use it to determine the critical line and the critical exponents that quantify the scaling behavior of different physical quantities. The critical line and the critical exponents are shown to be gauge invariant to O(1/N).

Ultraviolet fixed point structure of renormalizable four-fermion theory in less than four dimensions

We study the renormalization properties of the four-fermion theory in less than four dimensions (D<4) in the 1/N expansion scheme. It is shown that the β function of the bare coupling has a nontrivial ultraviolet fixed point with a large anomalous dimension (γ m = D−2) in a similar manner to QED and the gauged Nambu-Jona-Lasinio (NJL) model. The anomalous dimension has no discontinuity across the fixed point in sharp contrast to the gauged NJL model. The operator product expansion of the fermion mass function is also given.