Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Phase structure of twisted Eguchi-Kawai model

Tatsuo Azeyanagi, Masanori Hanada, Tomoyoshi Hirata, Tomomi Ishikawa

Abstract

Twisted Eguchi-Kawai model is a useful tool for studying the large-N gauge theory. It can also provide a nonperturbative formulation of the gauge theory on noncommutative spaces. Recently it was found that the Z_N^4 symmetry in this model, which is crucial for the above applications, can break spontaneously in the intermediate coupling region. In this article, we study the phase structure of this model using the Monte-Carlo simulation. In particular, we elaborately investigate the symmetry breaking point from the weak coupling side. The simulation results show that we cannot take a continuum limit for this model.

Phase structure of twisted Eguchi-Kawai model

Abstract

Twisted Eguchi-Kawai model is a useful tool for studying the large-N gauge theory. It can also provide a nonperturbative formulation of the gauge theory on noncommutative spaces. Recently it was found that the Z_N^4 symmetry in this model, which is crucial for the above applications, can break spontaneously in the intermediate coupling region. In this article, we study the phase structure of this model using the Monte-Carlo simulation. In particular, we elaborately investigate the symmetry breaking point from the weak coupling side. The simulation results show that we cannot take a continuum limit for this model.

Paper Structure

This paper contains 14 sections, 40 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Twisted Eguchi-Kawai model
  3. Action and Wilson loop
  4. Twist prescriptions and classical solutions
  5. $\mathbb{Z}_N^4$ symmetry
  6. Limiting procedure
  7. $\mathbb{Z}_N^4$ symmetry breaking in the TEK model
  8. Simulation method
  9. Simulation results
  10. Discussions
  11. Theoretical estimation of the $\mathbb{Z}_N^4$ symmetry breaking point
  12. Continuum and large-$N$ limit
  13. Conclusions
  14. Double scaling limit as the noncommutative Yang-Mills theory

Figures (4)

  • Figure 1: Plot of $\beta_c^L$ versus $N$ for the minimal symmetric twist. Fit line is equation (\ref{['EQ:bc_L_minimal_sym']}), which is obtained using $N\geq169$ data.
  • Figure 2: Expectation value of the plaquette (top) and the Polyakov line (besides the top) versus the lattice coupling $\beta$ for $N=100$ with the minimal skew-diagonal twist (cold start). As $\beta$ is decreased, the $\mathbb{Z}_N^4$ symmetry is broken and restored as $\mathbb{Z}_N^4\leftarrow\mathbb{Z}_N^3\leftarrow \mathbb{Z}_N^2\leftarrow\mathbb{Z}_N^0\xleftarrow{\beta_c^L} \mathbb{Z}_N^4$.
  • Figure 3:
  • Figure 5: