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.
Highlights
A perturbative calculation in gauge theories requires gauge fixing
A single zero mode In Ref. [27], a single zero mode was found in an instanton background
We introduce a field φ(x), and replace ic · ∂μDμc with ic · [∂μDμ + gφ×]c
Summary
A perturbative calculation in gauge theories requires gauge fixing. in nonAbelian gauge theories, there is a problem of gauge copies [1]. The boundary that the lowest eigenvalue of the FP operator equals zero is called the (first) Gribov horizon ∂Ω. More restricted region in Ω, that is called a fundamental modular region (FMR) Λ, is considered [5].) Another idea is to sum over all gauge copies [6, 7]. Gauge configurations on the Gribov horizon contribute in general, and the FP operator has zero modes. These zero modes can cause a trouble in proving the gauge equivalence [12]. In Appendix D, symmetries in the nonlinear gauge are discussed
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