$Z_3$ Twisted Chiral Condensates in QCD at Finite Temperatures

It was recently observed in a lattice QCD measurement that the chiral condensate in the quenched approximation shows dramatically different behavior in the three $Z_3$-equivalent de-confined phases. We argue that this phenomenon can be understood qualitatively as an effect of $Z_3$ twists on fermionic fields. Quarks under these $Z_3$-twists become global anyons and hence display different thermodynamic properties. We further show that the lattice data can be roughly modeled by a Nambu-Jona-Lasinio type Lagrangian with a minimal coupling to a constant gauge field $A_0=2\pi nT/3$ (with $n=0$, $\pm1$), which arises naturally from the non-trivial phase of the Polyakov line.