Polyakov Loops, Z(N) Symmetry, and Sine-Law Scaling

Details Polyakov Loops, Z(N) Symmetry, and Sine-Law Scaling Polyakov Loops, Z(N) Symmetry, and Sine-Law Scaling

2004-09-21

arxiv.org/abs/hep-lat/0409136v1

Physics

High Energy Physics

High Energy Physics - Lattice

Talk presented at Lattice2004(topology), Fermilab, June 21-26, 2004, 3 pages

Scientific paper

10.1016/j.nuclphysbps.2004.11.12

We construct an effective action for Polyakov loops using the eigenvalues of the Polyakov loops as the fundamental variables. We assume Z(N) symmetry in the confined phase, a finite difference in energy densities between the confined and deconfined phases as $T\to 0$, and a smooth connection to perturbation theory for large $T$. The low-temperature phase consists of $N-1$ independent fields fluctuating around an explicitly Z(N) symmetric background. In the low-temperature phase, the effective action yields non-zero string tensions for all representations with non-trivial $N$-ality. Mixing occurs naturally between representations of the same $N$-ality. Sine-law scaling emerges as a special case, associated with nearest-neighbor interactions between Polyakov loop eigenvalues.

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