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

Authors
Type
Preprint
Publication Date
Sep 21, 2004
Submission Date
Sep 21, 2004
Identifiers
DOI: 10.1016/j.nuclphysbps.2004.11.120
Source
arXiv
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.