Controls

Polyakov loop:
L = (1/N_c) Tr P exp(i∫₀^β A₀dτ)

⟨L⟩ = 0 → confined
⟨L⟩ ≠ 0 → deconfined

Z(N_c) symmetry:
Spontaneously broken above T_c. First-order for pure gauge (N_c≥3).

Cross-over:
With dynamical quarks: smooth crossover at T_c ≈ 155 MeV.