Gauge invariant effective action for the Polyakov line in the SU(N) Yang-Mills theory at high temperatures -: art. no. 105016

We integrate out fast varying quantum fluctuations around static A(4) and A(i) fields for the SU(N) gauge group. By assuming that the gluon fields are slowly varying but allowing for an arbitrary amplitude of A(4) we obtain two variants of the effective high-temperature theory for the Polyakov line. One is the effective action for the gauge-invariant eigenvalues of the Polyakov line, and it is explicitly Z(N) symmetric. The other is the effective action for the Polyakov line itself as an element of the SU(N). In this case the theory necessarily includes the spatial components A(i) to ensure its gauge invariance under spatial gauge transformations. We derive the 1-loop effective action in the electric and magnetic sectors, summing up all powers of A(4).