Polyakov loops, Z(N) symmetry, and sine-law scaling

We construct an effective action for Polyakov loops using the eigenvalues of the Polyakov loops as the fun- damental variables. We assume Z(N) symmetry in the confined phase, a finite difference in energy densities between the confined and deconfined phases as T → 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.