Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

't Hooft and Wilson loop ratios in the QCD plasma

P. Giovannangeli, C. P. Korthals Altes

Abstract

The spatial 't Hooft loop measuring the electric flux and the spatial Wilsonloop measuring the magnetic flux are analyzed in hot SU(N) gauge theory. Both display area laws. On one hand the tension of the 't Hooft loop is perturbatively calculable, in the same sense as the pressure. We show that the O(g^3) contribution is absent. The ratio of multi-charged 't Hooft loops have a remarkably simple dependence on the charge, true up to, but not including, O(g^4). This dependence follows also from a simple model of free screened colour charges. On the other hand the surface tension of the Wilsonloop is non-perturbative. But in a model of screened free monopoles at very high temperature the known area law follows. The density of these monopoles starts to contribute to O(g^6) to the pressure. The ratio of the multicharged Wilson loops is calculable and identical to that of the 't Hooft loops.

't Hooft and Wilson loop ratios in the QCD plasma

Abstract

The spatial 't Hooft loop measuring the electric flux and the spatial Wilsonloop measuring the magnetic flux are analyzed in hot SU(N) gauge theory. Both display area laws. On one hand the tension of the 't Hooft loop is perturbatively calculable, in the same sense as the pressure. We show that the O(g^3) contribution is absent. The ratio of multi-charged 't Hooft loops have a remarkably simple dependence on the charge, true up to, but not including, O(g^4). This dependence follows also from a simple model of free screened colour charges. On the other hand the surface tension of the Wilsonloop is non-perturbative. But in a model of screened free monopoles at very high temperature the known area law follows. The density of these monopoles starts to contribute to O(g^6) to the pressure. The ratio of the multicharged Wilson loops is calculable and identical to that of the 't Hooft loops.

Paper Structure

This paper contains 18 sections, 81 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Elementary facts
  3. A simple analysis of the 't Hooft loop tension
  4. The quantitative approach
  5. Effective potential and Wilsonline correlators
  6. One loop ratio
  7. Two loop ratio
  8. The potential term in two loop order
  9. The kinetic term to two loop order
  10. The kinetic energy at small values of the profile
  11. The electric QCD action with a gauge invariant infrared cut-off
  12. Calculation of the kinetic energy term for small profile with ${\cal{L}}_E$
  13. Why there are no $O(g^3)$ contribution to the surface tension
  14. A numerical exploration of the absolute minimum for SU(4)
  15. A simple and less simplistic approach to the ratios
  16. ...and 3 more sections

Figures (8)

  • Figure 1: Profile of the Wilson line phase for 't Hooft loop in the x-y plane at $z=0$ (continuous line). This profile minimizes $U(C)$. The broken line is the translate of the right hand branch by the $\theta$-function in eq.(\ref{['eq:boundary']}) in the text, and gives the profile one gets by minimizing $U(C)$ between two Z(N) minima at $C=0$ and $C={2\pi\over N}TY$.
  • Figure 2: Minimizing the effective action $U=K+V$ with two different boundary conditions. The continuous curve corresponds to that of the jump of the 't Hooft loop between ${\pi\over N}$ and $-{\pi\over N}$. The continuous-dotted curve corresponds to the boundary conditions of the domain wall.
  • Figure 3: The two diagrams with the mixed constraint/conventional vertices, giving the mass $m_{cc}^2$ in eq. (\ref{['eq:mixed']}). In the loops are only hard modes
  • Figure 4: Leading contribution to the kinetic energy of the profile (wavy line). Curly line is the $Q_z$, straight line the $Q_0$ propagator.
  • Figure 5: The complex k plane and the onset of the branchcuts for the graph in fig.(\ref{['fig:graph']})
  • ...and 3 more figures