Lattice Landau gauge with stochastic quantisation

TL;DR

This paper uses stochastic quantisation to compute Landau gauge ghost and gluon propagators in SU(2) lattice gauge theory across multiple dimensions, comparing it with standard methods and analyzing the Faddeev-Popov spectrum.

Contribution

It demonstrates stochastic quantisation as a viable alternative for gauge fixing and explores its effects on sampling near the Gribov horizon compared to standard techniques.

Findings

Stochastic quantisation samples configurations near the Gribov horizon at low accuracy.

Standard gauge fixing aligns with stochastic results at high accuracy.

Reproduces known lattice results for propagators in multiple dimensions.

Abstract

We calculate Landau gauge ghost and gluon propagators in pure SU(2) lattice gauge theory in two, three and four dimensions. The gauge fixing method we use, sc. stochastic quantisation, serves as a viable alternative approach to standard gauge fixing algorithms. We also investigate the spectrum of the Faddeev-Popov operator. At insufficiently accurate gauge fixing, we find evidence that stochastic quantisation samples configurations close to the Gribov horizon. Standard gauge fixing does so only at specific parameters; otherwise, there is a clear difference. However, this difference disappears if the gauge is fixed to sufficient accuracy. In this case, we confirm previous lattice results for the gluon and ghost propagator in two, three and four dimensions.