Dynamical Mass Generation Research Articles

Dynamical supergravity breaking via the super-Higgs effect revisited

We investigate the dynamical breaking of local supersymmetry (supergravity), including the Deser-Zumino super-Higgs effect, via the corresponding one-loop effective potential for the simple but quite representative cases of N=1, D=4 simple supergravity and a (simplified) conformal version of it. We find solutions to the effective equations which indicate dynamical generation of a gravitino mass, thus breaking supergravity. In the case of conformal supergravity models, the gravitino mass can be much lower than the Planck scale, for global supersymmetry breaking scales below the Grand Unification scale. The absence of instabilities in the effective potential arising from the quantum fluctuations of the metric field is emphasised, contrary to previous claims in the literature.

Dynamical Masses and Confinement in Graphene

Dynamical Mass Generation and Confinement are non-perturbative phenomena with large impact on the study of hadron and condensed matter physics. We study these phenomena in the light of the Schwinger-Dyson equations in various field theories, like Quantum Electrodynamics (QED) and Quantum Electrodynamics in the plane (QED3). Our aim is to describe the impact of these phenomena for the semi-metal–insulator transition in graphene, which is modeled by a peculiar field theory that inherits properties of both QED and QED3.

ONE-DIMENSIONAL QUANTUM LATTICE BOLTZMANN SCHEME FOR THE NONLINEAR DIRAC EQUATION

We develop a quantum lattice Boltzmann (QLB) scheme for the Dirac equation with a nonlinear fermion interaction provided by the Nambu–Jona-Lasinio (NJL) model. Numerical simulations in 1 + 1 space-time dimensions, provide evidence of dynamic mass generation, through spontaneous breaking of chiral symmetry.

Multiple solutions for the fermion mass function in QED3

Theories that support dynamical generation of a fermion mass gap are of widespread interest. The phenomenon is often studied via the Dyson-Schwinger equation (DSE) for the fermion self energy; i.e., the gap equation. When the rainbow truncation of that equation supports dynamical mass generation, it typically also possesses a countable infinity of simultaneous solutions for the dressed-fermion mass function, solutions which may be ordered by the number of zeros they exhibit. These features can be understood via the theory of nonlinear Hammerstein integral equations. Using QED3 as an example, we demonstrate the existence of a large class of gap equation truncations that possess solutions with damped oscillations. We suggest that there is a larger class, quite probably including the exact theory, which does not. The structure of the dressed-fermion--gauge-boson vertex is an important factor in deciding the issue.

Bootstrap dynamical symmetry breaking with strong Yukawa coupling

The newly discovered 126 GeV boson appears, by all counts, to be the Higgs boson of the Standard Model. Although this seems to exclude the existence of a heavy fourth generation quark doublet Q, for theoretical interest, we document a mechanism of dynamical mass generation via strong Yukawa coupling. The Goldstone boson G (the longitudinal component of the weak boson) couples to Q with Yukawa coupling λ Q . A “bootstrap” gap equation is constructed, where strong λ Q generates large quark mass m Q , thereby breaks electroweak symmetry breaking while self-consistently justifying G as a massless Goldstone particle in the loop. We solve the gap equation numerically and find m Q to be a couple of TeV. Putting in the light Higgs boson raises the strength of λ Q considerably, hence m Q as well, and does not look viable. But the equation allows for a dilaton of scale invariance violation, which has weaker coupling than the Higgs boson, except for gg and γγ modes. Whether a dilaton can be still compatible with current data is relegated to an appendix.

Intermediate effective interactions and dynamical fermion mass generation of QCD

The functional renormalization group equation is expanded to a two-loop form. This two-loop form equation involves one-loop effective action. An intermediate effective action perspective is adopted toward the one-loop effective action. That is to say, the intermediate effective action could not be of the same form of the bare action and one can make an ansatz to it. Thus by focusing on different high-dimensional operators, effects of the chosen operators can be investigated. QCD through intermediate 4-fermion interactions is investigated. Of the six kinds of 4-fermion interactions generated by one-loop QCD, four kinds generate fermion mass while the other two kinds decrease it. Flow patterns on the ${\stackrel{\texttildelow{}}{m}}_{\mathrm{phys}}^{2}\ensuremath{-}{\stackrel{\texttildelow{}}{g}}^{2}$ plane are drawn.

Dynamical mass generation of vector mesons from QCD trace anomaly

Mass formulas for the light-vector mesons written in terms of the gluon condensate i.e., the trace anomaly in quantum chromodynamics (QCD), are derived on the basis of finite energy QCD sum rules. We utilize sum rules with $s^n$ and $s^{n+1/2}$ weights, which relate the energy-weighted spectral sums to the vacuum expectation values of certain commutation relations. After evaluating the commutation relations, the sum rules with $s^n$ weights are reduced to the familiar ones obtained from the operator product expansion (OPE). On the other hand, the sum rules with $s^{n+1/2}$ weights cannot be derived from OPE. They give new relations between the spectral sums and QCD vacuum fluctuations. To derive simple mass formula, we adopt the pole + continuum Ansatz for the spectral function, and solve coupled equations given by the sum rules with $s^{0,1}$ weights and the new sum rule with $s^{1/2}$ weight. Application of our approach to the axial-vector meson is also discussed.

Quark propagation in the instantons of lattice QCD

We quantitatively examine the extent to which instanton degrees of freedom, contained within standard Monte-Carlo generated gauge-field configurations, can maintain the characteristic features of the mass and renormalization functions of the nonperturbative quark propagator. We use over-improved stout-link smearing to isolate instanton effects on the lattice. Using a variety of measures, we illustrate how gauge fields consisting almost solely of instantonlike objects are produced after only 50 sweeps of smearing. We find a full vacuum, with a packing fraction more than three times larger than phenomenological models predict. We calculate the overlap quark propagator on these smeared configurations, and find that even at high levels of smearing the majority of the characteristic features of the propagator are reproduced. We thus conclude that instantons contained within standard Monte-Carlo generated gauge-field configurations are the degrees of freedom responsible for the dynamical generation of mass observed in lattice QCD.

Dynamical mass generation of composite Dirac fermions and fractional quantum Hall effects near charge neutrality in graphene

We develop a composite Dirac fermion theory for the fractional quantum Hall effects (QHE) near charge neutrality in graphene. We show that the interactions between the composite Dirac fermions lead to a dynamical mass generation through exciton condensation. The four-fold spin–valley degeneracy is fully lifted due to the mass generation and exchange effects such that the odd-denominator fractional QHE observed in the vicinity of charge neutrality can be understood in terms of the integer QHE of composite Dirac fermions. At a filling factor ν = 1/2, we show that the massive composite Dirac fermion liquid is unstable against chiral p-wave pairing for weak Coulomb interactions and the ground state is a paired non-Abelian quantum Hall state described by the Moore–Read Pfaffian in the long wavelength limit.

Majorana versus Dirac mass from holomorphic supersymmetric Nambu–Jona-Lasinio model

We study the theoretical features in relation to dynamical mass generation and symmetry breaking for the recently proposed holomorphic supersymmetric Nambu--Jona-Lasinio model. The basic model has two different chiral superfields (multiplets) with a strongly coupled dimension five four-superfield interaction. In addition to the possibility of generation of Dirac mass between the pair established earlier, we show here the new option of generation of Majorana masses for each chiral superfield. We also give a first look at what condition may prefer Dirac over Majorana mass, illustrating that a split in the soft supersymmetry breaking masses is crucial. In particular, in the limit where one of the soft masses vanish, we show that generation of the Majorana mass is no longer an option, while the Dirac mass generation survives well. The latter is sensitive mostly to the average of the two soft masses. The result has positive implication on the application of the model framework towards dynamical electroweak symmetry breaking with Higgs superfields as composites.

Two-loop effective potential for the Wess-Zumino model in2+1dimensions

By using superfield techniques, the effective potential of the $\mathcal{N}=1$ Wess-Zumino model in 2+1 dimensions is computed off-shell up to two loops. It is shown that supersymmetry is not dynamically broken, and that dynamical generation of mass does not occur perturbatively. We also investigate the renormalization of the effective potential and determine the renormalization group gamma and beta functions, showing that this model is infrared free. Comparison with some other results in the literature is provided.

S-parameter, technimesons, and phase transitions in holographic tachyon DBI models

We investigate some phenomenological aspects of the holographic models based on the tachyon Dirac-Born-Infeld action in anti--de Sitter space-time. These holographic theories model strongly interacting fermions and feature dynamical mass generation and symmetry breaking. We show that they can be viewed as models of holographic walking technicolor and compute the Peskin-Takeuchi $S$ parameter and masses of lightest technimesons for a variety of tachyon potentials. We also investigate the phase structure at finite temperature and charge density. Finally, we comment on the holographic Wilsonian renormalization group in the context of holographic tachyon Dirac-Born-Infeld models.

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

We study chiral symmetry breaking for fundamental charged fermions coupled electromagnetically to photons with the inclusion of a four-fermion contact self-interaction term, characterized by coupling strengths $\ensuremath{\alpha}$ and $\ensuremath{\lambda}$, respectively. We employ multiplicatively renormalizable models for the photon dressing function and the electron-photon vertex that minimally ensures mass anomalous dimension ${\ensuremath{\gamma}}_{m}=1$. 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 ${N}_{f}={N}_{f}^{c}$ above which chiral symmetry is restored. This effect is in diametrical opposition to the existence of criticality for the minimum interaction strengths, ${\ensuremath{\alpha}}_{c}$ and ${\ensuremath{\lambda}}_{c}$, 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 $\ensuremath{\alpha}$ and the four-fermion coupling $\ensuremath{\lambda}$, 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 nonlinearized gap equation. A three-dimensional critical surface is drawn in the phase space of $(\ensuremath{\alpha},\ensuremath{\lambda},{N}_{f})$ to clearly depict the interplay of their relative strengths to separate the two phases. We also compute the $\ensuremath{\beta}$ functions (${\ensuremath{\beta}}_{\ensuremath{\alpha}}$ and ${\ensuremath{\beta}}_{\ensuremath{\lambda}}$) and observe that ${\ensuremath{\alpha}}_{c}$ and ${\ensuremath{\lambda}}_{c}$ are their respective ultraviolet fixed points. The power law part of the momentum dependence, describing the mass function, implies ${\ensuremath{\gamma}}_{m}=1+s$, which reproduces the quenched limit trivially. We also comment on the continuum limit and the triviality of QED.

DYNAMICAL SYMMETRY BREAKING IN A MINIMAL 3-3-1 MODEL

The gauge symmetry breaking in some versions of 3-3-1 models can be implemented dynamically because at the scale of a few TeVs the U(1)X coupling constant becomes strong. In this work, we consider the dynamical symmetry breaking in a minimal SU(3) TC × SU(3)L × U(1)X model, where we propose a new scheme to cancel the chiral anomalies, including two-index symmetric (6) technifermions, which incorporates naturally the walking behavior in the Technicolor (TC) sector. The composite scalar content of the model is minimal and all the symmetry breaking is implemented by a multiplet of technifermions. The choice of TC representations not only provides the anomaly cancelation with a walking behavior, but is crucial to promote the model's full dynamical symmetry breaking. We consider the dynamical generation of technigluon masses and, depending on the 3-3-1 symmetry breaking scale (μ331), we verify that the technigluon mass is strongly linked to the Z′ mass scale, for instance, if μ331 = 1 TeV , we have MZ′ > 1 TeV only if M TG < 350 GeV .

SU(3)center vortices underpin confinement and dynamical chiral symmetry breaking

The mass function of the nonperturbative quark propagator in SU(3) gauge theory shows only a weak dependence on the vortex content of the gauge configurations. Of particular note is the survival of dynamical mass generation on vortex-free configurations having a vanishing string tension. This admits the possibility that mass generation associated with dynamical chiral symmetry breaking persists without confinement. In this presentation, we examine the low-lying ground-state hadron spectrum of the pi, rho, N and Delta and discover that while dynamical mass generation persists in the vortex-free theory, it is not connected to dynamical chiral symmetry breaking. In this way, centre vortices in SU(3) gauge theory are intimately linked to both confinement and dynamical chiral symmetry breaking. We conclude that centre vortices are the essential underlying feature of the QCD vacuum.

Higher-order corrections in a four-fermion Lifshitz model

We study a flavor-violating four-fermion interaction in the Lifshitz context, in $3+1$ dimensions and with a critical exponent $z=3$. This model is renormalizable, and features dynamical mass generation, as well as asymptotic freedom. At one-loop, it is only logarithmically divergent, but the superficial degree of divergence of the two-point functions is 3. We calculate the two-loop corrections to the propagators, and show that, at this order, the Lorentz-violating corrections to the IR dispersion relation are quadratic in the cut off. Furthermore, these corrections are too significant to represent a physical effect. As a consequence, the predictive power of the model in terms of Lorentz-violating effects in the propagation of particles is limited.

Dynamical generation of mass in the noncommutative supersymmetric Schwinger model

Within the superfield formalism, we study the dynamical generation of mass to the gauge superfield in the noncommutative two-dimensional supersymmetric Schwinger model. We show that the radiatively generated mass for the gauge superfield does not depend on the noncommutative parameter $\ensuremath{\Theta}$ up to one-loop order.

Chiral symmetry breaking in planar QED in external magnetic fields

We investigate planar quantum electrodynamics (QED) with two degenerate staggered fermions in an external magnetic field on the lattice. We argue that in external magnetic fields there is dynamical generation of mass for two-dimensional massless Dirac fermions in the weak-coupling region. We extrapolate our lattice results to the quantum Hall effect in graphene.

Influence of Fermion Velocity Renormalization on Dynamical Mass Generation in QED3

We study dynamical fermion mass generation in (2 + 1)-dimensional quantum electrodynamics with a gauge field coupling to massless Dirac fermions and non-relativistic scalar bosons. We calculate the fermion velocity renormalization and then examine its influence on dynamical mass generation by using the Dyson—Schwinger equation. It is found that dynamical mass generation takes place even after including the scalar bosons as long as the bosonic compressibility parameter ξ is sufficiently small. In addition, the fermion velocity renormalization enhances the dynamically generated mass.

THE QUANTUM HALL EFFECT IN GRAPHENE

We investigate the quantum Hall effect in graphene. We argue that in graphene in presence of an external magnetic field there is dynamical generation of mass by a rearrangement of the Dirac sea. We show that the mechanism breaks the lattice valley degeneracy only for the n = 0 Landau levels and leads to the new observed ν = ±1 quantum Hall plateaus. We suggest that our result can be tested by means of numerical simulations of planar Quantum Electro Dynamics with dynamical fermions in an external magnetic fields on the lattice.