# The Gribov Horizon and Ghost Interactions in Euclidean Gauge Theories

## TL;DR

This paper investigates how the Gribov horizon influences ghost interactions in Euclidean SU(2) gauge theory, revealing ghost condensation and gauge behavior changes in the infrared limit.

## Contribution

It demonstrates that ghost zero modes induced by the Gribov horizon lead to additional ghost interactions and a nonlinear gauge, with recovery of Landau gauge in the infrared.

## Key findings

- Ghost zero modes produce additional interactions.
- Ghost condensation occurs in nonlinear gauges.
- Landau gauge is recovered in the infrared limit.

## Abstract

The effect of the Gribov horizon in Euclidean $SU(2)$ gauge theory is studied. Gauge fields on the Gribov horizon yield zero modes of ghosts and anti-ghosts. We show these zero modes can produce additional ghost interactions, and the Landau gauge changes to a nonlinear gauge effectively. In the infrared limit, however, the Landau gauge is recovered, and ghost zero modes may appear again. We show ghost condensation happens in the nonlinear gauge, and the zero mode repetition is avoided.