Coulomb gauge vacua of SU(3) gauge theory

SU(3) gauge field theory is studied in the Coulomb gauge, and the topologically distinct, but gauge equivalent, vacuum configurations are analysed. Considering the gauge transformations of the form U ε U(2) ?SU(3)/U(2), we have obtained a new class of vacuum fields characterized by the topological quantum number η = ±1.     

3-dimensionalSU(2) lattice gauge theory in terms of gauge invariant variables

As a first step towards a duality transformation for theSU(2) lattice gauge theory in 3 dimensions, the integration over all gauge variant variables is performed explicitly after introducing gauge invariant auxiliary variables. The resulting new Hamiltonian is complex and involves a sum over closed loops. Each of these loops is confined to an elementary cube of a dual lattice. Like in a previous investigation for theO(4) symmetric Heisenberg ferromagnet Rühl's boson representation is used to derive the result.     

Trimuons in SU(3) gauge models

We discuss models of weak interactions which can account for the recently observed μ^?μ^?μ⁺ events in v_μ reactions by allowing for the production of a new heavy neutral lepton and a new quark. One model is based on an SU(3) × U(1) gauge theory in shich the left-handed leptons are classified in anti-triplets. The second model catagorizes the leptons in an octet in accord with the more restrictive SU(3) weak gauge theory.     

Abelian 3-form gauge theory: Superfield approach

We discuss a D-dimensional Abelian 3-form gauge theory within the framework of Bonora-Tonin’s superfield formalism and derive the off-shell nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for this theory. To pay our homage to Victor I. Ogievetsky (1928–1996), who was one of the inventors of Abelian 2-form (antisymmetric tensor) gauge field, we go a step further and discuss the above D-dimensional Abelian 3-form gauge theory within the framework of BRST formalism and establish that the existence of the (anti-)BRST invariant Curci-Ferrari (CF) type of restrictions is the hallmark of any arbitrary p-form gauge theory (discussed within the framework of BRST formalism).     

Truncated Schwinger-Dyson equations and gauge covariance in QED3

We study the Landau-Khalatnikov-Fradkin transformations (LKFT) in momentum space for the dynamically generated mass function in QED3. Starting from the Landau gauge results in the rainbow approximation, we construct solutions in other covariant gauges. We confirm that the chiral condensate is gauge invariant as the structure of the LKFT predicts. We also check that the gauge dependence of the constituent fermion mass is considerably reduced as compared to the one obtained directly by solving SDE. Correspondence: A. Bashir, Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Apartado Postal 2-82, Morelia, Michoacán 58040, México     

Scaling behaviour of SU(3) gauge theory

Recent data of Monte Carlo simulations of SU(3) pure gauge theory are analyzed. The renormalization group structure is studied and asymptotic scaling is found to hold for β 6.0. Data are consistently described using a confining potential superimposed on a perturbative coulombic background. We find Λ/√σ = 0.0113 ± 0.004.     

Topological susceptibility in SU(3) gauge theory

We compute the topological susceptibility for the SU(3) Yang-Mills theory by employing the expression of the topological charge density operator suggested by Neuberger's fermions. In the continuum limit we find r(4)(0)chi = 0.059(3), which corresponds to chi = (191 +/- 5 MeV)(4) if F(K) is used to set the scale. Our result supports the Witten-Veneziano explanation for the large mass of the eta(').     

Thermodynamics of SU(3) lattice gauge theory

The pressure and the energy density of the SU(3) gauge theory are calculated on lattices with temporal extent N_τ = 4, 6 and 8 and spatial extent N_σ = 16 and 32. The results are then extrapolated to the continuum limit. In the investigated temperature range up to five times T_c we observe a 15% deviation from the ideal gas limit. We also present new results for the critical temperature on lattices with temporal extent N_τ = 8 and 12. At the corresponding critical couplings the string tension is calculated on 32⁴ lattices to fix the temperature scale. An extrapolation to the continuum limit yields T_c/√σ = 0.629(3). We furthermore present results on the electric and magnetic condensates as well as the temperature dependence of the spatial string tension. These observables suggest that the temperature dependent running coupling remains large even at T ≅ 5T_c. For the spatial string tension we find √σ_s/T=0.566(13)g²2(T) with g² (5T_c) ≅ 1.5.     

Zwanziger-Landau gauge in regularized gauge theory

The Green functions of Zwanziger-gaugefixed and continuum-regularized gauge theory are finite and transverse to all orders as the Zwanziger parameter α goes to zero.     

ISO(3, 1) gauge theory of gravity

We establish a Poincaré affine frame bundle, give the operation of gauge groupISO(3, 1) on the fiber bundle, obtain the action of the Poincaré gauge theory of gravity, and advance two sets of gravitational gauge field equations of the theory. We discuss some special cases of the theory.     

Light-cone gauge formulation for AdS 4 × ℂℙ3 superstring

We review the Type IIA superstring on the AdS ₄ × ??³ background in the κ-symmetry light-cone gauge characterized by the choice of the light-like directions from the D = 3 Minkowski boundary of AdS ₄ both in the Lagrangian and Hamiltonian formulations.     

Fixed twist dynamics of SO(3) gauge theory

We perform a thorough study of 3+1-dimensional SO(3) LGT for fixed-twist background. We concentrate in particular on the physically significant trivial and 1-twist sectors. Introducing a ℤ₂ monopole chemical potential the 1st order bulk transition is moved down in the strong coupling region and weakened to 2nd order in the 4-dimensional Ising model universality class. In this extended phase diagram we gain access to a confined phase in every fixed-twist sector of the theory. The Pisa disorder operator is employed together with the Polyakov loop to study the confinement–deconfinement transition in each sector. Due to the specific properties of both operators, most results can be used to gain insight in the ergodic theory, where all twist sectors should be summed upon. An explicit mapping of each fixed-twist theory to effective positive plaquette models with fixed-twisted boundary conditions is applied to better establish their properties in the different phases.     

String tension in SU(3) lattice gauge theory

Wilson loop expectation values have been determined in SU(3) lattice gauge theory without fermions using Monte Carlo methods and considering lattices of up to 10⁴ sites. A heat bath technique has been developed in order to enhance the statistical independence of successive lattice configurations.     

Dual-BRST symmetry: 6D Abelian 3-form gauge theory

Within the framework of the Becchi–Rouet–Stora–Tyutin (BRST) formalism, we demonstrate the existence of the novel off-shell nilpotent (anti-)dual-BRST symmetries in the context of a six (5+1)-dimensional (6D) free Abelian 3-form gauge theory. Under these local and continuous symmetry transformations, the total gauge-fixing term of the Lagrangian density remains invariant. This observation should be contrasted with the off-shell nilpotent (anti-)BRST symmetry transformations, under which, the total kinetic term of the theory remains invariant. The anticommutator of the above nilpotent (anti-)BRST and (anti-)dual-BRST transformations leads to the derivation of a bosonic symmetry in the theory. There exists a discrete symmetry transformation in the theory which provides a thread of connection between the nilpotent (anti-)BRST and (anti-)dual-BRST transformations. This theory is endowed with a ghost-scale symmetry, too. We discuss the algebra of these symmetry transformations and show that the structure of the algebra is reminiscent of the algebra of de Rham cohomological operators of differential geometry.