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The Confinement Problem in Lattice Gauge Theory

J. Greensite

Abstract

I review investigations of the quark confinement mechanism that have been carried out in the framework of SU(N) lattice gauge theory. The special role of Z(N) center symmetry is emphasized.

The Confinement Problem in Lattice Gauge Theory

Abstract

I review investigations of the quark confinement mechanism that have been carried out in the framework of SU(N) lattice gauge theory. The special role of Z(N) center symmetry is emphasized.

Paper Structure

This paper contains 52 sections, 256 equations, 44 figures, 1 table.

Table of Contents

  1. Introduction
  2. What is Confinement?
  3. Regge Trajectories and Color Fields
  4. A First Encounter with the Center
  5. Signals of the Confinement Phase
  6. The Wilson Loop
  7. The Polyakov Line
  8. The 't Hooft Operator
  9. The Vortex Free Energy
  10. Confinement Without Center Symmetry?
  11. The Case of SO(3) Gauge Theory
  12. Properties of the Confining Force
  13. Linearity
  14. Casimir Scaling
  15. N-ality Dependence
  16. ...and 37 more sections

Figures (44)

  • Figure 1: In both QCD with dynamical quarks, and in a theory with complete spontaneous symmetry breaking, the field of a static color source $Q$ in the fundamental representation is completely screened.
  • Figure 2: Regge trajectories for the low-lying mesons (figure from Bali, ref. Bali0).
  • Figure 3: String breaking by quark-antiquark pair production.
  • Figure 4: The global center transformation. Each of the indicated links in the $t$-direction, at $t=t_0$, is multiplied by a center element $z$. The lattice action is left unchanged by this operation.
  • Figure 5: A loop topologically linked to: a) a point, $D=2$; b) another loop, $D=3$; 4) a surface, $D=4$.
  • ...and 39 more figures