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W. Franzki

Publications and source records attributed to W. Franzki.

18 recordsLinked to original sources
arXiv1998

New universality class of chiral symmetry breaking in the strongly coupled U(1) $χU ϕ$ model

We describe a 4D U(1) lattice gauge theory with charged scalar $ϕ$ and fermion $χ$ matter fields ($χU ϕ$ model). At sufficiently strong gauge coupling, the chiral symmetry is broken and the mass of the unconfined composite fermion $F = \barχ ϕ$ is generated dynamically by gauge interaction. The scalar supresses this symmetry breaking and induces a line of second order transitions with scaling properties similar to the Nambu--Jona-Lasinio model. However, in the vicinity of a particular, tricritical point the scaling properties are different. Here we study the effective Yukawa coupling between the massive fermion and the Goldstone boson. The perturbative triviality bound of Yukawa models is nearly saturated. The theory is similar to strongly coupled Yukawa models except the occurrence of an additional state -- a gauge ball of mass $m_S \simeq 1/2 m_F$. This, and non-classical values of tricritical exponents suggest that at the tricritical point the $χU ϕ$ model constitutes a new universality class. Nevertheless, it might be a microscopic model for the Higgs-Yukawa mechanism of symmetry breaking.

hep-lat↗
arXiv1998

Analysis of the Lee-Yang zeros in a dynamical mass generation model in three dimensions

We investigate a strongly U(1) gauge theory with fermions and scalars on a three dimensional lattice and analyze whether the cintinuum limit might be a renormalizable theory with dynamical mass generation. Most attention is paid to the weak coupling region where a possible new dynamical mass generation mechanism might exist. There we investigate the mass of the composite fermion, the chiral condensate and the scaling of the Lee-Yang zeros.

hep-lat↗
arXiv1998

Strongly coupled lattice gauge theory with dynamical fermion mass generation in three dimensions

We investigate the critical behaviour of a three-dimensional lattice $\chiUϕ_3$ model in the chiral limit. The model consists of a staggered fermion field, a U(1) gauge field (with coupling parameter $β$) and a complex scalar field (with hopping parameter $κ$). Two different methods are used: 1) fits of the chiral condensate and the mass of the neutral unconfined composite fermion to an equation of state and 2) finite size scaling investigations of the Lee-Yang zeros of the partition function in the complex fermion mass plane. For strong gauge coupling ($β< 1$) the critical exponents for the chiral phase transition are determined. We find strong indications that the chiral phase transition is in one universality class in this $β$ interval: that of the three-dimensional Gross-Neveu model with two fermions. Thus the continuum limit of the $\chiUϕ_3$ model defines here a nonperturbatively renormalizable gauge theory with dynamical mass generation. At weak gauge coupling and small $κ$, we explore a region in which the mass in the neutral fermion channel is large but the chiral condensate on finite lattices very small. If it does not vanish in the infinite volume limit, then a continuum limit with massive unconfined fermion might be possible in this region, too.

hep-lat↗
arXiv1997

Dynamical fermion mass generation at a tricritical point in strongly coupled U(1) lattice gauge theory

Fermion mass generation in the strongly coupled U(1) lattice gauge theory with fermion and scalar fields of equal charge is investigated by means of numerical simulation with dynamical fermions. Chiral symmetry of this model is broken by the gauge interaction and restored by the light scalar. We present evidence for the existence of a particular, tricritical point of the corresponding phase boundary where the continuum limit might possibly be constructed. It is of interest as a model for dynamical symmetry breaking and mass generation due to a strong gauge interaction. In addition to the massive and unconfined fermion F and Goldstone boson $π$, a gauge ball of mass $m_S \simeq 1/2 m_F$ and some other states are found. Tricritical exponents appear to be non-classical.

hep-lat↗
arXiv1997

Strongly coupled U(1) lattice gauge theory as a microscopic model of Yukawa theory

Dynamical chiral symmetry breaking in a strongly coupled U(1) lattice gauge model with charged fermions and scalar is investigated by numerical simulation. Several composite neutral states are observed, in particular a massive fermion. In the vicinity of the tricritical point of this model we study the effective Yukawa coupling between this fermion and the Goldstone boson. The perturbative triviality bound of Yukawa models is nearly saturated. The theory is quite similar to strongly coupled Yukawa models for sufficiently large coupling except the occurrence of an additional state -- a gauge ball of mass about half the mass of the fermion.

hep-lat↗
arXiv1997

Scaling of gauge balls and static potential in the confinement phase of the pure U(1) lattice gauge theory

We investigate the scaling behaviour of gauge-ball masses and static potential in the pure U(1) lattice gauge theory on toroidal lattices. An extended gauge field action $-\sum_P(β\cosΘ_P + γ\cos2Θ_P)$ is used with $γ= -0.2$ and -0.5. Gauge-ball correlation functions with all possible lattice quantum numbers are calculated. Most gauge-ball masses scale with the non-Gaussian exponent $ν_{ng}\approx 0.36$. The $A_1^{++}$ gauge-ball mass scales with the Gaussian value $ν_{g} \approx 0.5$ in the investigated range of correlation lengths. The static potential is examined with Sommer's method. The long range part scales consistently with $ν_{ng}$ but the short range part tends to yield smaller values of $ν$. The $β$-function, having a UV stable zero, is obtained from the running coupling. These results hold for both $γ$ values, supporting universality. Consequences for the continuum limit of the theory are discussed.

hep-lat↗
arXiv1997

Strongly coupled compact lattice QED with staggered fermions

We explore the compact U(1) lattice gauge theory with staggered fermions and gauge field action -\sum_P [β\cos(Θ_P) + γ\cos(2Θ_P)], both for dynamical fermions and in the quenched approximation. (Θ_P denotes the plaquette angle.) In simulations with dynamical fermions at various γ\le -0.2 on 6^4 lattices we find the energy gap at the phase transition of a size comparable to the pure gauge theory for γ\le 0 on the same lattice, diminishing with decreasing γ. This suggests a second order transition in the thermodynamic limit of the theory with fermions for γbelow some finite negative value. Studying the theory on large lattices at γ= -0.2 in the quenched approximation by means of the equation of state we find non-Gaussian values of the critical exponents associated with the chiral condensate, β\simeq 0.32 and δ\simeq 1.8, and determine the scaling function. Furthermore, we evaluate the meson spectrum and study the PCAC relation.

hep-lat↗
arXiv1997

Gauge-ball spectrum of the four-dimensional pure U(1) gauge theory

We investigate the continuum limit of the gauge-ball spectrum in the four-dimensional pure U(1) lattice gauge theory. In the confinement phase we identify various states scaling with the correlation length exponent $ν\simeq 0.35$. The square root of the string tension also scales with this exponent, which agrees with the non-Gaussian fixed point exponent recently found in the finite size studies of this theory. Possible scenarios for constructing a non-Gaussian continuum theory with the observed gauge-ball spectrum are discussed. The $0^{++}$ state, however, scales with a Gaussian value $ν\simeq 0.5$. This suggests the existence of a second, Gaussian continuum limit in the confinement phase and also the presence of a light or possibly massless scalar in the non-Gaussian continuum theory. In the Coulomb phase we find evidence for a few gauge-balls, being resonances in multi-photon channels; they seem to approach the continuum limit with as yet unknown critical exponents. The maximal value of the renormalized coupling in this phase is determined and its universality confirmed.

hep-lat↗
arXiv1996

Properties of the non-Gaussian fixed point in 4D compact U(1) lattice gauge theory

We examine selected properties of the gauge-ball spectrum and fermionic variables in the vicinity of the recently discussed non-Gaussian fixed point of 4D compact U(1) lattice gauge theory within the quenched approximation. Approaching the critical point from within the confinement phase, our data support scaling of $T1^{+-}$ gauge-ball states in units of the string tension square root. The analysis of the chiral condensate within the framework of a scaling form for the equation of state suggests non mean-field values for the magnetic exponents $δ$ and $β_{exp}$.

hep-lat↗
arXiv1996

Non-Gaussian fixed point candidates in the 4D compact U(1) gauge theories

Some interesting nonperturbative properties of the strongly coupled 4D compact U(1) lattice gauge theories, both without and with matter fields, are pointed out. We demonstrate that the pure gauge theory has a non-Gaussian fixed point with $ν= 0.365(8)$ at the second order confinement-Coulomb phase transition. Thus a non-asymptotic free and nontrivial continuum limit of this theory, and of its various dual equivalents, in particular of a special case of the effective string theory, can be constructed. Including a scalar matter field (compact scalar QED), we confirm the Gaussian behavior at the endpoint of the Higgs phase transition line. In the theory with both scalar and fermion matter fields, we demonstrate the existence of a tricritical point. Here, the chiral symmetry is broken, and the mass of unconfined composite fermions is generated dynamically. Appart from the Goldstone bosons, the spectrum contains also a massive scalar. This resembles the Higgs-Yukawa sector of the SM, albeit of dynamical origin, like the Nambu--Jona-Lasinio model. However, the scaling behavior is different from that in the NJL model and the nonperturbative renormalizability might thus be possible.

hep-lat↗
arXiv1996

Scaling behavior at the tricritical point in the fermion-gauge-scalar model

We investigate a strongly coupled U(1) gauge theory with fermions and scalars on the lattice and analyze whether the continuum limit might be a renormalizable theory with dynamical mass generation. Most attention is paid to the phase with broken chiral symmetry in the vicinity of the tricritical point found in the model. There we investigate the scaling of the masses of the composite fermion and of some bosonic bound states. As a by-product we confirm the mean-field exponents at the endpoint in the U(1)-Higgs model, by analyzing the scaling of the Fisher zeros.

hep-lat↗
arXiv1996

Two-dimensional model of dynamical fermion mass generation in strongly coupled gauge theories

We generalize the $N_F=2$ Schwinger model on the lattice by adding a charged scalar field. In this so-called $χUϕ_2$ model the scalar field shields the fermion charge, and a neutral fermion, acquiring mass dynamically, is present in the spectrum. We study numerically the mass of this fermion at various large fixed values of the gauge coupling by varying the effective four-fermion coupling, and find an indication that its scaling behavior is the same as that of the fermion mass in the chiral Gross-Neveu model. This suggests that the $χUϕ_2$ model is in the same universality class as the Gross-Neveu model, and thus renormalizable and asymptotic free at arbitrary strong gauge coupling.

hep-lat↗
arXiv1995

Gauge invariant generalization of the 2D chiral Gross-Neveu model

By means of the Lee-Shrock transformation we generalize the 2D Gross-Neveu (GN$_2$) model to a U(1) gauge theory with charged fermion and scalar fields in 2D ($χU ϕ_2$ model). The $χU ϕ_2$ model is equivalent to the GN$_2$ model at infinite gauge coupling. We show that the dynamical fermion mass generation and asymptotic freedom in the effective four-fermion coupling persist also when the gauge coupling decreases. These phenomena are not influenced by the XY$_2$ model phase transition at weak coupling. This suggests that the $χU ϕ_2$ model is in the same universality class as the GN$_2$ model and thus renormalizable.

hep-lat↗
arXiv1995

Tricritical point in strongly coupled U(1) gauge theory with fermions and scalars

We investigate the tricritical point in the lattice fermion--gauge--scalar model with U(1) gauge symmetry. In the vicinity of this point, in the phase with the broken chiral symmetry, we observe the scaling behavior of the chiral condensate and of the masses of composite fermion and composite scalar, indicating the existence of an interesting continuum limit of the model at this point.

hep-lat↗
arXiv1995

Chiral phase transition in a lattice fermion--gauge--scalar model with U(1) gauge symmetry

The chiral phase transition induced by a charged scalar field is investigated numerically in a lattice fermion-gauge-scalar model with U(1) gauge symmetry, proposed recently as a model for dynamical fermion mass generation. For very strong gauge coupling the transition is of second order and its scaling properties are very similar to those of the Nambu--Jona-Lasinio model. However, in the vicinity of the tricritical point at somewhat weaker coupling, where the transition changes the order, the scaling behavior is different. Therefore it is worthwhile to investigate the continuum limit of the model at this point.

hep-lat↗
arXiv1994

On the equivalence between 2D Yukawa and Gross-Neveu models

We study numerically on the lattice the 2D Yukawa model with the U(1) chiral symmetry and $N_F$ = 16 at infinite scalar field self-coupling. The scaling behaviour of the fermion mass, as the Yukawa coupling approaches zero, is analysed using the mean field method. It is found to agree with that of the Gross-Neveu model with the same symmetry and $N_F$. The results suggest that the 2D Yukawa models belong to the universality class of the Gross-Neveu models not only at weak scalar field self-coupling but also for a broad range of the bare parameters which is not accessible to the $1/N_F$ expansion. New universality classes might arise at the crossover to the spin model universality class, however.

hep-lat↗
arXiv1993

Study of the Asymptotic Freedom of 2D Yukawa Models on the Lattice

We investigate on the lattice the Yukawa models in 2 dimensions with Z(2) and U(1) symmetries. These models reduce to the usual and chiral Gross-Neveu models, respectively, when the kinetic and the selfcoupling terms of the scalar field are turned off. The numerical data and mean field arguments suggest that, at least for some range of the scalar field hopping parameter, fermion mass is dynamically generated for arbitrarily weak Yukawa coupling. The models are asymptotically free in this coupling, like the Gross-Neveu models, even when the scalar quartic selfcoupling is strong.

hep-lat↗