The strong-coupling limit of minimal lattice Landau gauge

TL;DR

This study investigates the infrared behavior of gluon and ghost propagators in lattice Landau gauge at strong coupling, revealing conformal behavior at large momenta and gauge-dependent deviations at low momenta, with implications for understanding non-perturbative QCD.

Contribution

It provides evidence of conformal infrared behavior of propagators in the strong-coupling limit of lattice gauge theory, highlighting gauge dependence and non-perturbative effects.

Findings

Conformal behavior appears at large momenta in the strong-coupling limit.

Deviations at low momenta are linked to a transverse gluon mass proportional to 1/a.

Deviations depend on the lattice definition of gauge fields, unlike the asymptotic behavior.

Abstract

We study the gluon and ghost propagators of lattice Landau gauge in the strong coupling limit $\beta = 0$ in pure SU(2) lattice gauge theory to find evidence of the conformal infrared behaviour of these propagators as predicted by a variety of functional continuum methods for asymptotically small momenta $q^2 \ll \Lambda_\mathrm{QCD}^2$. In the strong-coupling limit, this same behaviour is obtained for the larger values of $a^2q^2$ (in units of the lattice spacing $a$), where it is otherwise swamped by the gauge field dynamics. Deviations for $a^2 q^2 < 1 $ are well parametrized by a transverse gluon mass $\propto 1/a$. Perhaps unexpectedly, these deviations are thus no finite-volume effect but persist in the infinite-volume limit. They furthermore depend on the definition of gauge fields on the lattice, while the asymptotic conformal behaviour does not.