# Constraining the gauge-fixed Lagrangian in minimal Landau gauge

## TL;DR

This paper explores formulating a gauge-fixed Lagrangian in minimal Landau gauge by reconstructing Dyson-Schwinger equations, introduces an extra term needed for consistency, and provides new high-precision lattice results for the ghost-gluon vertex.

## Contribution

It proposes a constrained Lagrangian formulation in minimal Landau gauge and derives new lattice data for the ghost-gluon vertex.

## Key findings

- Reconstruction of Dyson-Schwinger equations requires an additional term.
- New high-precision lattice results for the ghost-gluon vertex in 3D and 4D.
- Insights into gauge-fixing and Gribov ambiguity in continuum and lattice formulations.

## Abstract

A continuum formulation of gauge-fixing resolving the Gribov-Singer ambiguity remains a challenge. Finding a Lagrangian formulation of operational resolutions in numerical lattice calculations, like minimal Landau gauge, would be one possibility. Such a formulation will here be constrained by reconstructing the Dyson-Schwinger equation for which the lattice minimal-Landau-gauge ghost propagator is a solution. It is found that this requires an additional term. As a by-product new, high precision lattice results for the ghost-gluon vertex in three and four dimensions are obtained.