On the irrelevance of the Gribov issue in N=4N=4 Super Yang–Mills in the Landau gauge

The issue of the Gribov copies is discussed in Euclidean N=4N=4 Super Yang–Mills theory quantized in the Landau gauge. As a consequence of the absence of a renormalization group invariant scale, it turns out that it is not possible to attach a dynamical meaning to the Gribov parameter. This implies that, in N=4N=4 Super Yang–Mills, there is no need for the restriction of the domain of integration in the functional integral to the Gribov region, and no non-perturbative dynamical scale is generated. This result is in agreement with the absence of a confining phase observed from the Coulomb behavior of the Wilson loop evaluated through the AdS/CFT correspondence. The non-renormalization theorem of the gluon–ghost–antighost vertex of the Landau gauge is also explicitly checked till three loops.