Static quark-antiquark pair in SU(2) gauge theory

We study singlet and triplet correlation functions of a static quark-antiquark pair defined through gauge invariant timelike Wilson loops and Polyakov loop correlators in finite temperature SU(2) gauge theory. We use the Luscher-Weisz multilevel algorithm, which allows us to calculate these correlators at very low temperatures. We observe that the naive separation of singlet and triplet states, in general, does not hold nonperturbatively; however, it is recovered in the limit of small separation, and the temperature dependence of the corresponding correlators is indeed very different.