U(3) four-dimensional lattice gauge theory and Monte Carlo calculations

Monte Carlo results for the pure U(3) lattice gauge theory on a 6⁴ lattice are reported. Wilson loops and the string tension are presented. The first-order phase transition in U(3) is reflected quite clearly in a discontinuity in the string tension at β = β_c. The U(1) factor of U(3) is extracted using the determinant of the Wilson loops. As expected, the U(1) component appears to deconfine at the phase transition..     

Monte Carlo studies of wilson loops in four-dimensional U(2) gauge theory

Wilson loops are calculated using Monte Carlo simulations for pure U(2) gauge theory on a 6⁴ lattice. The loops appear to contain an area law piece in both the high and low temperature regions. The string tension is discontinuous at β = β_c, where β_c is the critical inverse temperature. This suggests that the first-order phase transition in U(2) gauge theory is not a deconfining phase transition. The determinant of the Wilson loop, however, extracts the U(1) part of the theory and appears to lose the area law at low temperature.     

Nonabelian electric and magnetic flux in unified SU(5) gauge theory

We study the long-distance behaviour of pure unified SU(5) gauge theory in the limit when the electroweak subgroup is unbroken. We show that the symmetry breaking pattern SU(5)→SU(3)_c×SU(2)×U(1)_Y, with SU(3)_c and SU(2) ×U(1)_Y realized, respectively, in confining and coulombic phases, is a possible dynamical phase of the SU(5) theory. The proof relies on showing that the duality equation of 't Hooft, relating the electric and magnetic flux, is exactly satisfied for the above symmetry breaking pattern. The infrared structure of SU(5), broken down to SU(3)_c×SU(2)×U(1)_Y, is not self-dual.     

Phase transition ofSU(3) gauge theory at finite temperature

We present evidence for the presence of a phase transition inSU(3) lattice gauge theory at finite temperature using Monte-Carlo methods. An extrapolation to the continuum limit leads to the valueT _c =Λ_mom±15% for the critical temperature separating the two phases.     

Quasi-confinement in theSU(3)-gluon plasma

We investigate a phenomenological equation of state for the gluon plasma, which differs from the ideal gluon gas equation of state in three aspects: (a) it is assumed that gluons withlow momentum are subject to confining interactions anddo not contribute to the energy spectrum of free gluons; (b)only gluons withhigh momentum are considered as an ideal gas with perturbative corrections of orderO(α_s); (c) a non-perturbative vacuum pressure is included. We show that feature (a) allows for a reasonable perturbative treatment of the interaction between gluons with high momentum. The equation of state reproduces lattice data for the thermodynamical functions of theSU(3) pure gauge theory above the deconfinement transition temperatureT _c. This result suggests that a possible way to describe the gluon plasma is in terms of perturbatively interacting gluons and non-perturbative “glueball” states.     

Relations between the electromagnetic form factors of the 0−- and 1−-mesons from the collinear groupsSU(3)⊗SU(3)⊗U(1) andSU(6) W

The relations between the electromagnetic matrix elements of the 18 low lying pseudoscalar and vector mesons predicted by the collinear groupsSU(3)?SU(3)?U(1) andSU(6) _W are derived. Using the hermiticity of the electromagnetic current operator, charge conjugation invariance and invariance under the full Lorentz group andSU(3)-symmetry separately, all electromagnetic matrix elements of these mesons are described by seven independent real form factors. After combining space-time with intrinsic properties of the particles this number is reduced to four by the minimal collinear groupSU(3) ?SU(3) ?U(1) and to three bySU(6) _W which involves more speculative assumptions. In the limit of low momentum transfer the predictions of both models become identical, depending on three real quantities. No disagreement with experiment has been found, as far as a comparison is possible.     

Experimental Consequences of the Asymptotically Free SU(5)-Model

The experimental consequences of the asymptotically free SU(5)-theory are presented which make it possible to judge about its reliability. The phenomenology of the τ-lepton is analysed with special attention paid to the so-called exotic processes which must solve whether “light” or “heavy” the ν_τ-neutrino should be. These exotic processes are completely forbidden within standard SU(5) schemes. The problem of the finite mass of the e, μ-neutrino which is a four-component Dirac spinor interacting via the Zel'dovitch-Mahmound-Konopinski scheme is discussed. The finiteness of such neutrino mass is a peculiarity of the SU(5) theory under discussion, although its value is not fixed here in a unique way. The version of the theory wherein m_ν ≦ 10⁻³ eV is of especial interest since in this case the proton instability and the finite e, μ-neutrino mass are found to be explained in a common way as manifestations of the existence of superheavy leptoquark bosons in the theory. The possibility is pointed out to explain within the SU(5) theory under consideration the existing experimental situations concerning the search for parity violating effects in atoms. It is shown that the present SU(5) theory encounters no difficulty in this respect and can recommend itself to any experimental set of data, whereas the standard schemes of SU(5) unification cannot. Cosmological consequences of the asymptotically free SU(5) theory are briefly discussed and the latter is found to rather reasonably explain a number of facts about the very early evolution of the Universe.     

Proton decay induced by instantons inSU(5) grand unification

Instantons infinitesimally turned out of theSU _c (3) subspace of spontaneously brokenSU(5) gauge theory induce a baryon number violating interaction proportional 1/μ _X ² like heavy vector boson exchange, but with a different tensor structure.     

Phase portrait ofSU(5) grand unified model

The one-loop effective potential of theSU(5) model is investigated both in high and low temperature approximation. We find the regions of values of coupling constants and temperatures where theSU(5), theSU(4)×U(1) and theSU(3)×SU(2)×U(1) symmetric states are metastable. A general method of such an investigation is proposed. We observe that the domain structure of the Universe with the simultaneous existence of the gauge symmetriesSU(4)×U(1) andSU(3)×SU(2)×U(1) in different domains could take place.     

The nature of the transition in d = 4 U(1) lattice gauge theory

The phase transition for the d = 4 compact U(1) lattice gauge theory has been studied using the Monte Carlo renormalization-group method. A single relevant eigenvalue is observed on the Wilson axis. The MCRG estimate for the exponent v changes with the coupling β; an extrapolation towards β^∞_c provides an estimate v ∼ 0.42 rather than ∼ 0.33 as obtained by finite-size scaling. It is confirmed that loops of monopole current are the mechanism driving the transition. It is shown that at the transition the largest loop of monopole current undergoes a discontinuity in size and begins to span the lattice. On the basis of these findings, it is conjectured that on the Wilson axis the discontinuity is a finite-size effect.     

Elektromagnetische Übergänge imSU(3)-Modell

A method is developed how to calculate electromagnetic transition probabilities and selection rules forSU(3)-classified wave functions. For this purpose the transition operators of electric multipole radiation are expanded inSU(3)-tensors. The calculations are explicitly carried out forE1- andE2-radiation. ForB(E2)-values in (λ,0)-bands an analytic expression is obtained independent of the special form of the interaction. The results ofSU(3)-theory are compared with those of Hartree-Fock-calculations performed by other authors. An astonishing agreement is found.     

Comparison of lattice gauge theories with gauge groups Z2 and SU(2)

We study a model of a pure Yang Mills theory with gauge group SU(2) on a lattice in Euclidean space. We compare it with the model obtained by restricting variables to $\text{Z}$₂. An inequality relating expectation values of the Wilson loop integral in the two theories is established. It shows that confinement of static quarks is true in our SU(2) model whenever it holds for the corresponding $\text{Z}$₂-model. The SU(2) model is shown to have high and low temperature phases that are distinguished by a qualitatively different behavior of the 't Hooft disorder parameter.     

The onset of deconfinement inSU(2) lattice gauge theory

InSU(2) lattice gauge theory, we study deviations from ideal gas behaviour near the deconfinement point. On lattices of sizeN _σ ³ ×4,N _σ=8, 12, 18 and 26, we calculate the quantityΔ≡(ε?3P)/T ⁴. It increases sharply just aboveT _c , peaks atT/T _c =1.15 ±0.05 and then drops quickly. This form of behaviour is shown to be the consequence of a second order phase transition. Dynamically it could arise because just aboveT _c , the low momentum states of the system are remnant massive modes rather than deconfined massless gluons.     

Discrete symmetries in SO(N) grand unified groups and the survival hypothesis

The possibility of introducing the discrete symmetry D is studied, which along with SU^c(3) × SU_L(2) × U(1)-symmetry, remains after the breaking of SO(N) grand unified symmetry by the Higgs fields vevs ～ 10¹⁵ GeV. The D quantum number distinguishes the fermions coupled with W-bosons via left and right currents. As a result, the presence of low-mass fermions in the theory is provided.     

Calculation of the viscosity of SU(2) gluodynamics with the lattice simulation

The viscosity of SU(2) gluodynamics within the simulation of the lattice quantum chromodynamics at a temperature of T/T _c = 1.2 has been calculated with the Kubo formula relating the viscosity to the spectral function of the correlation function of the energy-momentum tensor. The correlation function of the energy-momentum tensor has been calculated using the numerical simulation of the lattice SU(2) gluodynamics on supercomputers.     

A supersymmetricSU(5)×U(1) model with natural gauge hierarchy

We present a supersymmetricSU(5)×U(1) model. This model has the following features. The gauge hierarchy is naturally generated by the quadratically divergent nature of the Fayet-IliopoulosD term. TheSU(5)×U(1) gauge symmetry breaks uniquely intoSU(3) _W ×SU(2) _c ×U(1) _y at an energy scale of 10^17–18GeV. The non-vanishing vacuum expectation value of an auxiliary field component ofU(1) gauge vector multiplet induces the breaking ofSU(2) _W ×U(1) _y . It gives a mass of 10^2–3GeV to scalar quarks and scalar leptons at the tree level. The renormalization group analysis shows that the color fine structure constant α _C (M _W ) becomes somewhat small and the Weinberg angle sin²θ _W (M _W ) somewhat too large in a simple version of the model.     

The SU(5) potential in desitter space

The one-loop effective potential for a minimal SU(5) theory is calculated on a curved DeSitter background spacetime. The stability of its extrema in the following subgroups is investigated: SU(4) × U(1), SU(3) × SU(2) × U(1), SU(3) × U(1) × U(1), SU(2) × SU(2) × U(1) × U(1). A combination of analytic and numerical methods is used to obtain phase diagrams for the model. In the inflationary universe, the curvature effects do not prevent a slide into the SU(4) × U(1) extremum.     

Higgs production inSU(2) c symmetric interactions

We study the sensitivity of Higgs production and decay processes to theSU(2) _c symmetric couplingsO _W andO _UW . Remarkable results are obtained in the case of γγ→H and for certain ratios of Higgs decay widths. We also discuss and complete previous results on unitarity constraints for such couplings.