Effective Potential for Polyakov Loops in Lattice QCD

Precise measurement of Polyakov loop correlation is important for finite temperature physics. First of all heavy quark potentials at finite temperature are obtained by measuring twoPolyakov-loop correlation functions. It is already well-known that we can obtain the QQ̄ potential below and above the critical temperature (TC) from this measurement. Due to the nonperturbative effects, however, there are still less-known quantities at intermediate temperature. For example the QQ̄ potential at finite temperature is generally written as V/T = −e/(RT ) exp(−μR), where T is temperature, R the distance between quarks, and e, d, μ are parameters. At very high temperature, perturbation theory predicts d = 2, while just above TC , lattice simulation gives the deviation from d = 2[1]. In relation to such a nonperturbative behavior at finite temperature, our main interest here is to derive an effective theory for Polyakov loops from lattice QCD. Recently new Polyakov loop model is proposed[2] regarding the deconfining phase transition in SU(N) gauge theory. It conjectures a relationship between the Polyakov loops and the pressure. The usual Polyakov loop l1 transforms under a global Z(N) transformation as l1 → e l1, with φ = 2πj/N(j = 1...N − 1). This means that l1 transforms as a field with charge one. On the other hand one can consider Polyakov loops with higher charge under a global Z(N) transformation. For example the charge two Polyakov loop is defined