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.Comment: 4 page

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.Comment: Talk presented at LATTICE96(other models), 4 page

New universality class of chiral symmetry breaking in the strongly coupled U(1) χUϕ\chi U \phi model

We describe a 4D U(1) lattice gauge theory with charged scalar $\phi$ and fermion $\chi$ matter fields ($\chi U \phi$ model). At sufficiently strong gauge coupling, the chiral symmetry is broken and the mass of the unconfined composite fermion $F = \bar{\chi} \phi$ 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 $\chi U \phi$ model constitutes a new universality class. Nevertheless, it might be a microscopic model for the Higgs-Yukawa mechanism of symmetry breaking.Comment: LATTICE98(yukawa

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.Comment: 3 pages,4 figures,talk presented at Lattice97(Edinburgh

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 $\chi U\phi_2$ 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 $\chi U\phi_2$ model is in the same universality class as the Gross-Neveu model, and thus renormalizable and asymptotic free at arbitrary strong gauge coupling.Comment: 18 pages, LaTeX2e, requires packages rotating.sty and curves.sty from CTA

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.Comment: Contribution to Lattice 95, LaTeX file (4 pages), 5 ps-figures appended (uuencoded

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

We investigate the critical behaviour of a three-dimensional lattice \chiU\phi_3 model in the chiral limit. The model consists of a staggered fermion field, a U(1) gauge field (with coupling parameter $\beta$) and a complex scalar field (with hopping parameter $\kappa$). 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 ($\beta < 1$) 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 $\beta$ interval: that of the three-dimensional Gross-Neveu model with two fermions. Thus the continuum limit of the \chiU\phi_3 model defines here a nonperturbatively renormalizable gauge theory with dynamical mass generation. At weak gauge coupling and small $\kappa$, 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.Comment: 27 pages, 16 figure

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 $\pi$, 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.Comment: 21 page

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 ($\chi U \phi_2$ model). The $\chi U \phi_2$ 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 $\chi U \phi_2$ model is in the same universality class as the GN$_2$ model and thus renormalizable.Comment: Contribution to Lattice 95, LaTeX file (4 pages), 4 ps-figures appended (uuencoded), abstract correcte