Polyakov Loop Models, Z(N) Symmetry, and Sine-Law Scaling
Abstract
We construct an effective action for Polyakov loops using the eigenvalues of the Polyakov loops as the fundamental variables. We assume
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.