Abstract
In light of the recently established BRST invariant formulation of the Gribov–Zwanziger theory, we show that Zwanziger's horizon function displays a universal character. More precisely, the correlation functions of local BRST invariant operators evaluated with the Yang–Mills action supplemented with a BRST invariant version of the Zwanziger's horizon function and quantized in an arbitrary class of covariant, color invariant and renormalizable gauges which reduce to the Landau gauge when all gauge parameters are set to zero, have a unique, gauge parameters independent result, corresponding to that of the Landau gauge when the restriction to the Gribov region Ω in the latter gauge is imposed. As such, thanks to the BRST invariance, the cut-off at the Gribov region Ω acquires a gauge independent meaning in the class of the physical correlators.
Highlights
The restriction to the region Ω has been put on firm basis due to the following properties [3]: i) Ω is bounded in all directions in field space
All gauge orbits cross Ω at least once. The latter implies that gauge configurations lying outside the region Ω are copies of configurations belonging to Ω, giving a well motivated support to expression (2), in the sense that it does take into account all physically different gauge configurations †
Equation (40) summarises the main result of the present work, stating that the correlation functions of local BRST invariant operators are independent of the gauge parameters entering the gauge fixing condition
Summary
Where O(x) ‡ stands for a generic gauge invariant operator Correlation functions of this type are of fundamental importance in order to unravel the physical content of the restriction to the Gribov region and of the Gribov–Zwanzgier action. The action (6) exhibits a soft breaking of the BRST invariance, which turns out to be proportional to the Gribov parameter γ [1] This feature does not jeopardize the renormalizability of the Gribov–Zwanziger action (6), it obscures the physical meaning of γ itself, which encodes the restriction to the region Ω. In Sect. we present the main results of this paper: a generalization of the Gribov–Zwanziger setup to an arbitrary class of covariant, color invariant and renormalizable gauge fixings which reduce to the Landau gauge when setting the gauge parameters to zero, providing a universal character to (the BRST invariant extension of) Zwanziger’s horizon function.
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