Free Energy of an SU(2) Model of (2+1)-dimensional QCD in the Constant Condensate Background

Gluon and quark contributions to the thermodynamic potential (free energy) of a (2+1)-dimensional QCD model at finite temperature in the background of a constant homogeneous chromomagnetic field H combined with A_0 condensate are calculated. The role of the tachyonic mode in the gluon energy spectrum is discussed. A possibility of the free energy global minimum generation at nonzero values of H and A_0 condensates is investigated.Comment: LaTeX 2e, 14 pages, 6 eps figures, some miscalculations were correcte

Weyl group, CP and the kink-like field configurations in the effective SU(3) gauge theory

Effective Lagrangian for pure Yang-Mills gauge fields invariant under the standard space-time and local gauge SU(3) transformations is considered. It is demonstrated that a set of twelve degenerated minima exists as soon as a nonzero gluon condensate is postulated. The minima are connected to each other by the parity transformations and Weyl group transformations associated with the color su(3) algebra. The presence of degenerated discrete minima in the effective potential leads to the solutions of the effective Euclidean equations of motion in the form of the kink-like gauge field configurations interpolating between different minima. Spectrum of charged scalar field in the kink background is discussed.Comment: 10 pages, 1 figure, added references for sections 1 and

The Savvidy ``ferromagnetic vacuum'' in three-dimensional lattice gauge theory

The vacuum effective potential of three-dimensional SU(2) lattice gauge theory in an applied color-magnetic field is computed over a wide range of field strengths. The background field is induced by an external current, as in continuum field theory. Scaling and finite volume effects are analyzed systematically. The first evidence from lattice simulations is obtained of the existence of a nontrivial minimum in the effective potential. This supports a ``ferromagnetic'' picture of gluon condensation, proposed by Savvidy on the basis of a one-loop calculation in (3+1)-dimensional QCD.Comment: 9pp (REVTEX manuscript). Postscript figures appende

To what distances do we know the confining potential?

We argue that asymptotically linear static potential is built in into the common procedure of extracting it from lattice Wilson loop measurements. To illustrate the point, we extract the potential by the standard lattice method in a model vacuum made of instantons. A beautiful infinitely rising linear potential is obtained in the case where the true potential is actually flattening. We argue that the flux tube formation might be also an artifact of the lattice procedure and not necessarily a measured physical effect. We conclude that at present the rising potential is known for sure up to no more than about 0.7 fm. It may explain why no screening has been clearly observed so far for adjoint sources and for fundamental sources but with dynamical fermions. Finally, we speculate on how confinement could be achieved even if the static potential in the pure glue theory is not infinitely rising.Comment: 16 pages, 5 figures. Additional arguments presented, a new figure and references adde

Perturbative expansions from Monte Carlo simulations at weak coupling: Wilson loops and the static-quark self-energy

Perturbative coefficients for Wilson loops and the static-quark self-energy are extracted from Monte Carlo simulations at weak coupling. The lattice volumes and couplings are chosen to ensure that the lattice momenta are all perturbative. Twisted boundary conditions are used to eliminate the effects of lattice zero modes and to suppress nonperturbative finite-volume effects due to Z(3) phases. Simulations of the Wilson gluon action are done with both periodic and twisted boundary conditions, and over a wide range of lattice volumes (from $3^4$ to $16^4$) and couplings (from $\beta \approx 9$ to $\beta \approx 60$). A high precision comparison is made between the simulation data and results from finite-volume lattice perturbation theory. The Monte Carlo results are shown to be in excellent agreement with perturbation theory through second order. New results for third-order coefficients for a number of Wilson loops and the static-quark self-energy are reported.Comment: 36 pages, 15 figures, REVTEX documen

(Anti-)self-dual homogeneous vacuum gluon field as an origin of confinement and SUL(NF)×SUR(NF)SU_L(N_F)\times SU_R(N_F) symmetry breaking in QCD

It is shown that an (anti-)self-dual homogeneous vacuum gluon field appears in a natural way within the problem of calculation of the QCD partition function in the form of Euclidean functional integral with periodic boundary conditions. There is no violation of cluster property within this formulation, nor are parity, color and rotational symmetries broken explicitly. The massless limit of the product of the quark masses and condensates, $m_f \langle \bar\psi_f \psi_f \rangle$, is calculated to all loop orders. This quantity does not vanish and is proportional to the gluon condensate appearing due to the nonzero strength of the vacuum gluon field. We conclude that the gluon condensate can be considered as an order parameter both for confinement and chiral symmetry breaking.Comment: 16 pages, LaTe

Perturbation theory vs. simulation for tadpole improvement factors in pure gauge theories

We calculate the mean link in Landau gauge for Wilson and improved SU(3) anisotropic gauge actions, using two loop perturbation theory and Monte Carlo simulation employing an accelerated Langevin algorithm. Twisted boundary conditions are employed, with a twist in all four lattice directions considerably improving the (Fourier accelerated) convergence to an improved lattice Landau gauge. Two loop perturbation theory is seen to predict the mean link extremely well even into the region of commonly simulated gauge couplings and so can be used remove the need for numerical tuning of self-consistent tadpole improvement factors. A three loop perturbative coefficient is inferred from the simulations and is found to be small. We show that finite size effects are small and argue likewise for (lattice) Gribov copies and double Dirac sheets.Comment: 13 pages of revtex

Confining Properties of the Homogeneous Self-Dual Field and the Effective Potential in SU(2) Yang-Mills Theory

We examine in non-Abelian gauge theory the heavy quark limit in the presence of the (anti-)self-dual homogeneous background field and see that a confining potential emerges, consistent with the Wilson criterion, although the potential is quadratic and not linear in the quark separation. This builds upon the well-known feature that propagators in such a background field are entire functions. The way in which deconfinement can occur at finite temperature is then studied in the static temporal gauge by calculation of the effective potential at high temperature. Finally we discuss the problems to be surmounted in setting up the calculation of the effective potential nonperturbatively on the lattice.Comment: 31 pages, LaTeX, expanded discussion and derivations in Sections 2 and

Prospectives

Tiré de: Prospectives, vol. 14, no 1-2, février/avril 1978.Titre de l'écran-titre (visionné le 24 janv. 2013