W. Franzki

GAUGE-BALL SPECTRUM OF THE FOUR-DIMENSIONAL PURE U(1) GAUGE THEORY

Abstract We ibvestigate 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 ⋍ 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 ⋍ 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.

Strongly coupled compact lattice QED with staggered fermions

Abstract We explore the compact U(1) lattice gauge theory with staggered fermions and gauge field action − Σ P [ β cos ( Θ P ) + γ cos (2 Θ P )], both for dynamical fermions and in the quenched approximation. ( Θ P denotes the plaquette angle.) In simulations with dynamical fermions at various γ ⩽ −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 ⩽ 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 γ below 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 X ≅ 0.32 and δ ≅ 1.8, and determine the scaling function. Furthermore, we evaluate the meson spectrum and study the PCAC relation.

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

We investigate the critical behaviour of a three-dimensional latticeU�3 model in the chiral limit. The model consists of a staggered fermion field, a U(1) gauge field (with coupling parameter �) and a complex scalar field (with hopping parameter �). 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 (� < 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 thisinterval: that of the three-dimensional Gross-Neveu model with two fermions. Thus the continuum limit of the �U�3 model defines here a nonperturbatively renormalizable gauge theory with dynamical mass generation. At weak gauge coupling and small �, 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.

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 −ΣP(βcosΘP+γcos2ΘP) 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 νng0.36. The A1++ gauge-ball mass scales with the Gaussian value νg0.5 in the investigated range of correlation lengths. The static potential is examined with Sommers method. The long range part scales consistently with νng 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.

Chiral transition and monopole percolation in lattice scalar QED with quenched fermions

We study the interplay between topological observables and chiral and Higgs transitions in lattice scalar QED with quenched fermions. Emphasis is put on the chiral transition line and magnetic monopole percolation at strong gauge coupling. We confirm that at infinite gauge coupling the chiral transition is described by mean field exponents. We find a rich and complicated behavior at the end point of the Higgs transition line which hampers a satisfactory analysis of the chiral transition. We study in detail an intermediate coupling, where the data are consistent both with a trivial chiral transition clearly separated from monopole percolation and with a chiral transition coincident with monopole percolation, and characterized by the same critical exponent

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

ensuremath{nu}ensuremath{simeq}0.65.

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

We discuss the relevance (or lack thereof) of these quenched results to our understanding of the

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

ensuremath{chi}U{ensuremath{varphi}}_{4}

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

model. We comment on the interplay of magnetic monopoles and fermion dynamics in more general contexts.

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

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. The 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