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.     

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.     

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.     

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.     

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.     

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.     

Untersuchungen der Struktur von „antiferroelektrischem”(NH4)2H3IO6 mit Kernresonanzmethoden

The orientations and asymmetry parameters of the EFG tensors at the different lattice sites of I¹²⁷ in (NH₄)₂H₃IO₆ have been determined by proton-iodine crossover relaxation at room temperature and at 94°K. Based on these results it was possible to prove the existence of superstructure for the hexagonala- andc-directions and to reduce the number of allowed space groups of the low temperature phase to two: \(R\overline 3 c\) andR32. In both space groups half of the hydrogen bonds remain symmetric and only half of them become asymmetric (ordered) on lowering the temperature through the phase transition, but only inR32 there are antipolar sublattices. The transition entropies calculated for this model of the hydrogen arrangement agree fairly well with the measured value. With the evidence available it is not possible to rule out one of the two space groups.     

SU(7) Electroweak unification

Electroweak unification is obtained in anSU(7) model at a mass scale 3×10¹⁰≦M≦3×10¹⁶ GeV's, with left-right symmetric subgroups and sin² θ _w (M)=3/8. BelowM, the model reduces toSU(3) _L ×SU(3) _R , the flavor sector of the “trinification theory” of Glashow et al., or of theE ₆ grand unified theory. This model predicts a natural massless neutrino, and fractionally charged leptons with masses in theM regime.     

Direct evidence for a Coulombic phase in monopole-suppressed SU(2) lattice gauge theory

Further evidence is presented for the existence of a non-confining phase at weak coupling in SU(2) lattice gauge theory. Using Monte Carlo simulations with the standard Wilson action, gauge-invariant SO(3)–Z2 monopoles, which are strong-coupling lattice artifacts, have been seen to undergo a percolation transition exactly at the phase transition previously seen using Coulomb gauge methods, with an infinite lattice critical point near β=3.2$\beta =3.2$. The theory with both Z2 vortices and monopoles and SO(3)–Z2 monopoles eliminated is simulated in the strong-coupling (β=0$\beta =0$) limit on lattices up to 60⁴. Here, as in the high-β phase of the Wilson-action theory, finite size scaling shows it spontaneously breaks the remnant symmetry left over after Coulomb gauge fixing. Such a symmetry breaking precludes the potential from having a linear term. The monopole restriction appears to prevent the transition to a confining phase at any β  . Direct measurement of the instantaneous Coulomb potential shows a Coulombic form with moderately running coupling possibly approaching an infrared fixed point of α∼1.4$\alpha \sim 1.4$. The Coulomb potential is measured to 50 lattice spacings and 2 fm. A short-distance fit to the 2-loop perturbative potential is used to set the scale. High precision at such long distances is made possible through the use of open boundary conditions, which was previously found to cut random and systematic errors of the Coulomb gauge fixing procedure dramatically. The Coulomb potential agrees with the gauge-invariant interquark potential measured with smeared Wilson loops on periodic lattices as far as the latter can be practically measured with similar statistics data.