Finite-temperature gluodynamics with test charges in various representations

We analytically investigate the finite-temperature gluodynamics with test charges, which transform under arbitrary representations of the group $SU(3)$, on an anisotropic lattice in the spherical model approximation. We demonstrate that at below-critical temperatures, the potential for arbitrary charges with trialities differing in sign increases linearly with the distance between the charges, while the potential for sources with zero trialities has the Debye form. The model predicts that the attractive Coulomb potential exists for all the representations, which indicates that bound states exist at all above-critical temperatures.