Gluon propagator and confinement scenario in Coulomb gauge

A particularly simple confinement scenario [1] is available in the minimal Coulomb gauge. It attributes confinement of color to the long range of the color-Coulomb potential Vcoul(R). This quantity is the instantaneous part of the 4-4 component of the gluon propagator, Dμν(x) ≡ 〈gAμ(x) gAν(0)〉, namely D44(x, t) = Vcoul(|x|)δ(t) +P (x, t). The vacuum polarization term P (x, t) is less singular than δ(t) at t = 0. Since A4 couples universally to color charge, the long range of Vcoul(R) suffices to confine all color charge. It was conjectured that it is linearly rising at large R, Vcoul(R) ∼ −σcoulR. If an external quark-antiquark pair is present, the physical potential VW(R) between them may be extracted from a Wilson loop. The color-Coulomb potential contributes the term −CVcoul(R) directly to the Wilson loop, where C = (N−1)/(2N) in SU(N) gauge theory with external quarks in the fundamental representation. The minus sign occurs because the antiquark has opposite charge to the quark. The vacuum-polarization term is screening, and one expects that VW(R) is bounded above by this term asymptotically at large R, VW(R) ≤ −CVcoul(R). If VW(R) is also linearly rising, VW(R) ∼ σR, where σ is the conventional