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

TL;DR

This paper argues that the Gribov problem is irrelevant in N=4 Super Yang-Mills theory in Landau gauge due to the lack of a dynamical scale, aligning with its non-confining nature observed via AdS/CFT.

Contribution

It demonstrates that the Gribov issue does not affect N=4 SYM in Landau gauge and confirms the non-renormalization of the gluon-ghost-antighost vertex up to three loops.

Findings

No dynamical scale is generated in N=4 SYM.

The Gribov parameter has no physical meaning in this context.

The non-renormalization theorem holds up to three loops.

Abstract

The issue of the Gribov copies is discussed in Euclidean N=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=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 behaviour 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.