An effective thermodynamic potential from the instanton vacuum with the Polyakov loop

In this talk, we report our recent studies on an effective thermodynamic potential (Omega_eff) at finite temperature (T>0) and zero quark-chemical potential (mu_R=0), using the singular-gauge instanton solution and Matsubara formula for N_c=3 and N_f=2 in the chiral limit, i.e. m_q=0. The momentum-dependent constituent-quark mass is computed as a function of T, together with the Harrington-Shepard caloron solution in the large-N_c limit. In addition, we take into account the imaginary quark-chemical potential mu_I = A_4, indentified as the traced Polayakov-loop (Phi) as an order parameter for the Z(N_c) symmetry, characterizing the confinement (intact) and deconfinement (spontaneously broken) phases. As a consequence, we observe the crossover of the chiral (chi) order parameter sigma^2 and Phi. It also turns out that the critical temperature for the deconfinement phase transition, T^Z_c is lowered by about (5~10) % in comparison to the case with the constant constituent-quark mass. This behavior can be understood by considerable effects from the partial chiral restoration and nontrivial QCD vacuum on the Phi. Numerical results show that the crossover transitions occur at (T^chi_c,T^Z_c) ~ (216,227) MeV.