Center vortices and confinement vs. screening

Abstract

We study adjoint and fundamental Wilson loops in the center-vortex picture of confinement, for gauge group SU(N) with general N. There are N-1 distinct vortices, whose properties, including collective coordinates and actions, we study. In d=2 we construct a center-vortex model by hand so that it has a smooth large-N limit of fundamental-representation Wilson loops and find, as expected, confinement. Extending an earlier work by the author, we construct the adjoint Wilson-loop potential in this d=2 model for all N, as an expansion in powers of $\rho /M^2$, where $\rho$ is the vortex density per unit area and M is the vortex inverse size, and find, as expected, screening. The leading term of the adjoint potential shows a roughly linear regime followed by string breaking when the potential energy is about 2M. This leading potential is a universal (N-independent at fixed fundamental string tension $K_F$) of the form $(K_F/M)U(MR)$, where R is the spacelike dimension of a rectangular Wilson loop. The linear-regime slope is not necessarily related to $K_F$ by Casimir scaling. We show that in d=2 the dilute vortex model is essentially equivalent to true d=2 QCD, but that this is not so for adjoint representations; arguments to the contrary are based on illegal cumulant expansions which fail to represent the necessary periodicity of the Wilson loop in the vortex flux. Most of our arguments are expected to hold in d=3,4 also.

29 pages, LaTex, 1 figure. Minor changes; references added; discussion of factorization sharpened. Major conclusions unchanged

References in corpus (3)

• Casimir Scaling from Center Vortices: Towards an Understanding of the Adjoint String Tension
• Vortices and confinement at weak coupling
• On One-Loop Gap Equations for the Magnetic Mass in d=3 Gauge Theory

Cited by in corpus (23)

• Gluon and ghost propagators in the Landau gauge: Deriving lattice results from Schwinger-Dyson equations
• Casimir scaling of SU(3) static potentials
• Detection of Center Vortices in the Lattice Yang-Mills Vacuum
• Gluon mass generation without seagull divergences
• Center Vortices, Nexuses, and the Georgi-Glashow Model
• Indirect determination of the Kugo-Ojima function from lattice data
• Center Vortices, Nexuses, and Fractional Topological Charge
• Nexus solitons in the center vortex picture of QCD
• Free energy of an SU(2) monopole-antimonopole pair
• A model for QCD ground state with magnetic disorder
• A conjecture on the infrared structure of the vacuum Schrodinger wave functional of QCD
• On the Structure of the Observable Algebra of QCD on the Lattice
• Static forces in d=2+1 SU(N) gauge theories
• Gluon mass scale through the Schwinger mechanism
• Free energy of an SU(2) monopole-antimonopole pair
• Entropy in quantum chromodynamics
• Effect of magnetic screening mass on the diffusion of heavy quarks
• Schwinger-Dyson equations and disorder
• $\beta$-function for topologically massive gluons
• Probing the center-vortex area law in d=3: The role of inert vortices
• A three-dimensional scalar field theory model of center vortices and its relation to k-string tensions
• Three easy exercises in off-shell string-inspired methods
• Multivacuum States in a Fermionic Gap Equation with massive gluons and confinement