Gauge dynamics in the PNJL model: Color neutrality and Casimir scaling

Understand

We discuss a gauge-invariant prescription to take the mean-field approximation self-consistently in the PNJL model (Nambu--Jona-Lasinio model with the Polyakov loop).

• We first address the problem of non-vanishing color density in normal quark matter, which is an artifact arising from gauge-fixed treatment of the Polyakov loop mean-fields.
• We then confirm that the gauge average incorporated in our prescription resolves this problem and ensures color neutrality.
• We point out that the proposed method has an advantage in computing the expectation value of any function of the Polyakov loop matrix.