Sweep-sweep correlations of polyakov loops for SU(3) lattice gauge theory on 324 lattices

The sweep-to-sweep correlations of Polyakov loops are calculated at β-values of 6.3, 6.6 and 6.9 on a 32⁴ lattice for SU(3) gauge theory. The distance versus correlation relations are determined. Confinement of adjoint sources is verified.     

Testing the rotational symmetry of theSU(3) potential

We test the static quark-antiquark potential inSU(3) lattice gauge theory, at β=5.8 on a 16⁴ lattice. We find an anisotropy on the level of 3% for small distances,r?3a. We discuss the implications of this effect on the determination of the string tension.     

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.     

Potentials in pure QCD on 324 lattices

A range of properties of pure SU (3) gauge theory are studied numerically on euclidean lattices of 32⁴ points at β values of 6.29, 6.585 and 6.88. Potentials between static pairs of colour charges in the triplet, octet and sextet representations are calculated. The lowest energy (the A_1g) gluonic modes are considered for each of these plus the E_u mode for the triplet case. In the calculations, the use of extended operators on the lattice is examined. The results are assessed for scaling but do not agree adequately with asymptotic behaviour based on the two-loop β-function.     

Wilson loops and constant gauge fields

We have computed the Wilson loop averaged over the class of constants gauge fields in two dimensions forSU(N), withN large. The limitN→∞ gives asymptotically an “area law” when the area of the loop tends to the total finite volume of space.     

Simple construction ofSU(3) representations using theSU(2) projection technique

SU(3) representations for theSU(3) SU(2) chain are constructed in a new way usingSU(2) projection operators. TheSU(3) D-functions, presented in new parametrizations, are expressed in terms ofSU(2) D-functions and 6j-symbols.Valuable discussions with Dr. J. Niederle are gratefully acknowledged.     

Wilson loops for U(4) and SU(4) lattice gauge theories in four dimensions

Monte Carlo simulations are used to calculate Wilson loops for pure U(4) and SU(4) gauge theories on a 6⁴ lattice. The first-order phase transitions previously observed in the average action per plaquette for U(4) and SU(4) is also seen in the string tension. U(4) and SU(4) color seem to be confined while U(4) charge in U(4) appears to be deconfined.     

Classical polylogarithms for amplitudes and Wilson loops

We present a compact analytic formula for the two-loop six-particle maximally helicity violating remainder function (equivalently, the two-loop lightlike hexagon Wilson loop) in N=4 supersymmetric Yang-Mills theory in terms of the classical polylogarithm functions Lik with cross ratios of momentum twistor invariants as their arguments. In deriving our formula we rely on results from the theory of motives.     

Planar and non-planar Wilson loops in QCD

A general QCD sum rule calculation of vacuum expectation values of Wilson loops is presented and particularized to several specific planar and non-planar contours. The string tension obtained is √σ = 0.50(5) GeV. Within the errors of the approach, this result is shape-independent. We comment on the possibility that corrections to the area and perimeter laws could be parametrized by a geodesic curvature term.     

Rigorous perimeter law upper bound on Wilson loops

We present a proof that in an arbitrary lattice gauge theory, the expectation value of a Wilson loop decays at least as fast as the exponential of the perimeter.     

Thermodynamics of theSU(N) anderson impurity

The thermodynamic Bethe-ansatz equations of the degenerate Anderson model in theU limit with excluded multiple occupation of the localized level are solved numerically for the casesN=2, 3, 4, and 6. The f-level occupation, the entropy, the spin and charge susceptibilities and the specific heat are obtained as a function of temperature for variousf-level energies.Heisenberg-fellow of the Deutsche Forschungsgemeinschaft     

Thermodynamics of theSU(N) Anderson impurity

The thermodynamic Bethe-ansatz equations of the degenerate Anderson model in theU limit with excluded multiple occupation of the localized level are solved numerically for the caseN=8. Thef-level occupation, the entropy, the spin and charge susceptibilities and the specific heat are obtained as a function of temperature for variousf-level energies. The results forN=6 andN=8 are compared with available data for CeTh and YbCuAl.     

Wilson loops,geometric operators and fermions in 3d group field theory

Group field theories whose Feynman diagrams describe 3d gravity with a varying configuration of Wilson loop observables and 3d gravity with volume observables at each vertex are defined. The volume observables are created by the usual spin network grasping operators which require the introduction of vector fields on the group. We then use this to define group field theories that give a previously defined spin foam model for fermion fields coupled to gravity, and the simpler “quenched” approximation, by using tensor fields on the group. The group field theory naturally includes the sum over fermionic loops at each order of the perturbation theory.     

Dipole solutions in theSU(2) andSU(3) gauge theory with electric and magnetic sources

The magnetic dipole solutions of Sikivie and Weiss are considered with the addition of a magnetic source and the validity of the observation that for large source strengths the energy of such solutions is lower than the energy of corresponding Coulomb solutions is examined. It is found that the presence of electric and magnetic sources leads to dipole solutions and that the introduction of a magnetic source does not alter the relationship between their energy and the energy of corresponding Coulomb solutions.     

Thermodynamics of theSU(N) Anderson impurity

The thermodynamic Bethe-ansatz equations of the degenerate Anderson model are derived in theU» limit, where the multiple occupation of the localized level is excluded. The Kondo (Coqblin-Schrieffer) limit and the Fermi liquid behavior at lowT are extracted from these equations.     

Hedgehogs in Wilson loops and phase transition in SU(2) Yang–Mills theory

We suggest that the gauge-invariant hedgehog-like structures in the Wilson loops are physically interesting degrees of freedom in the Yang–Mills theory. The trajectories of these “hedgehog loops” are closed curves corresponding to center-valued (untraced) Wilson loops and are characterized by the center charge and winding number. We show numerically in the SU(2) Yang–Mills theory that the density of hedgehog structures in the thermal Wilson–Polyakov line is very sensitive to the finite-temperature phase transition. The (additively normalized) hedgehog line density behaves like an order parameter: The density is almost independent of the temperature in the confinement phase and changes substantially as the system enters the deconfinement phase. In particular, our results suggest that the (static) hedgehog lines may be relevant degrees of freedom around the deconfinement transition and thus affect evolution of the quark–gluon plasma in high-energy heavy-ion collisions.     

Mass operator in theSU(3)-symmetric strong coupling theory with pseudoscalar mesons

In this paper theSU(3)-symmetric model of a static baryon octet source interacting with pseudoscalar meson octet fields by the coupling of Yukawa type is considered in the strong coupling limit. Using the result derived earlier that the isobaric states form the basis of the unitary irreducible representation of the dynamical group G=T ₂₄ [SU(3) SU(2)], the mass operator is specified by the kinetic part of the Hamiltonian as a particular element of the universal enveloping algebra of the symmetry groupSU(3) SU(2) acting in the space of isobaric states.