Renormalization of strongly coupled U(1) lattice gauge theories

Recent numerical studies of the 4D pure compact U(1) lattice gauge theory, I have participated in, are reviewed. We look for a possibility to construct an interesting nonperturbatively renormalizable continuum theory at the phase transition between the confinement and Coulomb phases. First I describe the numerical evidence, obtained from calculation of bulk observables on spherical lattices, that the theory has a non-Gaussian fixed point. Further the gauge-ball spectrum in the confinement phase is presented and its universality confirmed. The unexpected result is that, in addition to massive states, the theory contains a very light, possibly massless scalar gauge ball. I also summarize results of studies of the compact U(1) lattice theory with fermion and scalar matter fields and point out that at strong coupling it represents a model of dynamical fermion mass generation.Comment: Talk presented at the 31st International Symposium Ahrenshoop on the Theory of Elementary Particles, Buckow, September 2-6, 1997. 8 page

Interplay of universality classes in a three-dimensional Yukawa model

We investigate numerically on the lattice the interplay of universality classes of the three-dimensional Yukawa model with U(1) chiral symmetry, using the Binder method of finite size scaling. At zero Yukawa coupling the scaling related to the magnetic Wilson--Fisher fixed point is confirmed. At sufficiently strong Yukawa coupling the dominance of the chiral fixed point associated with the 3D Gross--Neveu model is observed for various values of the coupling parameters, including infinite scalar selfcoupling. In both cases the Binder method works consistently in a broad range of lattice sizes. However, when the Yukawa coupling is decreased the finite size behavior gets complicated and the Binder method gives inconsistent results for different lattice sizes. This signals a cross-over between the universality classes of the two fixed points.Comment: 24 pp. LaTeX 2e src, needs psfig.st

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

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

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.Comment: LaTeX, 11 pages (including 4 postscript figures); OUTP-93-01P (HLRZ 93-15

Observation of String Breaking in QCD

We numerically investigate the transition of the static quark-antiquark string into a static-light meson-antimeson system. Improving noise reduction techniques, we are able to resolve the signature of string breaking dynamics for n_f=2 lattice QCD at zero temperature. This result can be related to properties of quarkonium systems. We also study short-distance interactions between two static-light mesons.Comment: 27 pages, 22 figures, changed decimal place of errors in 3 entries of Table, corrected reference

Finite Size Analysis of the U(1) Phase Transition using the World-sheet Formulation

We present a high statistics analysis of the pure gauge compact U(1) lattice theory using the the world-sheet or Lagrangian loop representation. We have applied a simulation method that deals directly with (gauge invariant) integer variables on plaquettes. As a result we get a significant amelioration of the simulation that allows to work with large lattices avoiding the metaestability problems that appear using the standard Wilson formulation.Comment: 14 pages, 4 figures. REVTEX and eps

Dirac Relation and Renormalization Group Equations for Electric and Magnetic Fine Structure Constants

The quantum field theory describing electric and magnetic charges and revealing a dual symmetry was developed in the Zwanziger formalism. The renormalization group (RG) equations for both fine structure constants - electric $\alpha$ and magnetic $\tilde \alpha$ - were obtained. It was shown that the Dirac relation is valid for the renormalized $\alpha$ and $\tilde \alpha$ at the arbitrary scale, but these RG equations can be considered perturbatively only in the small region: $0.25 \stackrel{<}{\sim} \alpha, \tilde \alpha \stackrel{<}{\sim} 1$ with $\tilde \alpha$ given by the Dirac relation: $\alpha {\tilde \alpha}$ = 1/4.Comment: 15 pages, 4 figures, made corrections of physics after comments from Kim Milto

THE CRITICAL EXPONENTS OF THE DECONFINEMENT TRANSITION IN SU(2) LATTICE GAUGE-THEORY

Engels J, JERSAK J, KANAYA K, et al. THE CRITICAL EXPONENTS OF THE DECONFINEMENT TRANSITION IN SU(2) LATTICE GAUGE-THEORY. NUCLEAR PHYSICS B. 1987;280(4):577-598