Narrow Results

Recent progress on the calculation of the – potential is reviewed. Scaling is discussed from the perspective of critical phenomenon. Methods for fitting the correlations of Polyakov operators and the Wilson loops are reviewed and two new methods, the iterative method and the improved ratio method, are discussed in detail. These new methods are used to analyze/re-analyze the previously published data on Polyakov loops and new data on large Wilson loops. Convincing numerical evidences together with several analytical arguments strongly support the conclusion that the asymptotic scaling sets in at β~6 with and α=0.43±0.03. These results agree well with the potential model analysis of experimental data on and systems, and favors the Neveu-Schwarz strings as the underlying string theory. Finally, key issues on the use of the parallel computers are explored, with the conclusion that parallel computers are highly suitable for these floating-point intensive computations.

The screening length in a quark–gluon plasma, the dispersion relations of thermal gluon self-energy and the quark potential at high temperature are studied within the thermo field dynamics framework. By calculating the real and imaginary parts, of the gluon self-energy in one-loop order in thermo field dynamics, we obtain an expression for the screening length in a quark–gluon plasma and the dispersion relation between the real and imaginary parts. At high temperature, using photon exchange between electron-positron in a skeleton expansion and ladder approximation, the screened Coulomb potential and an expression for the screened quark potential is obtained.

Following a recently proposed confinement generating mechanism, we provide a new string inspired model with a massive dilaton and a new dilaton coupling function ⁵. By solving analytically the equations of motion, a new class of confining interquark potentials is derived which includes several popular potential forms given in the literature.

Some recent work on the implications of a dilaton in 4d gauge theories are revisited. In part I of this paper we see how an effective dilaton coupling to gauge kinetic term provides a simple attractive mechanism to generate confinement. In particular, we put emphasis on the derivation of confining analytical solutions and look into the problem how dilaton degrees of freedom modify Coulom potential and when a confining phase occurs. In part II, we solve the semi-relativistic wave equation, for Dick interquark potential using the Shifted l-expansion technique (SLET) in the heavy quarkonium sector. The results of this phenomenological analysis proves that these effective theories can be relevant to model quark confinement and may shed some light on confinement mechanism.

The confinement problem is studied using the thick center vortex model. It is shown that the $SU(3)$ Cartan subalgebra of the decomposed $G(2)$ gauge theory can play an important role in the confinement. The Casimir eigenvalues and ratios of the $G(2)$ representations are obtained using its decomposition to the $SU(3)$ subgroups. This leads to the conjecture that the $SU(3)$ subgroups also can explain the $G(2)$ properties of the confinement. The thick center vortex model for the $SU(3)$ subgroups of the $G(2)$ gauge theory is applied without the domain modification. Instead, the presence of two $SU(3)$ vortices with opposite fluxes due to the possibility of decomposition of the $G(2)$ Cartan subalgebra to the $SU(3)$ groups can explain the properties of the confinement of the $G(2)$ group both at intermediate and asymptotic distances which is studied here.