Non-perturbative formulation of the static color octet potential

By dressing Polyakov lines with appropriate functionals of the gauge fields, we construct observables describing a fundamental representation static quark–antiquark pair in the singlet, adjoint and average channels of SU(N) pure gauge theory. Each of the potentials represents a gauge invariant eigenvalue of the Hamiltonian. Numerical simulations are performed for SU(2) in 2+1 dimensions. The adjoint channel is found to be repulsive at small and confining at large separations, suggesting the existence of a metastable (N2−1)-plet bound state. For small distances and temperatures above the deconfinement transition, the leading order perturbative prediction for the ratio of singlet and adjoint potentials is reproduced by the lattice data.