Creutz Ratios From Color-Truncated Lattice Configurations

TL;DR

This paper explores whether Creutz ratios in lattice gauge theory can be reconstructed from individual gluon color components by abelianizing the configurations, showing that the ratios converge to the standard values.

Contribution

It demonstrates that abelianized gluon configurations retain the essential Creutz ratio information, providing a new perspective on color component contributions in lattice gauge theory.

Findings

Creutz ratios from abelianized configurations converge to standard ratios

Color component reduction preserves key gauge-invariant information

Rescaling compensates for loss of fluctuation in abelianization process

Abstract

We investigate whether information about Creutz ratios is encoded, separately, in each gluon color component of numerically generated lattice configurations. Working in SU(2) lattice gauge theory in Landau gauge, we set two of the three gluon color components to zero, and compensate for the loss of two-thirds of the fluctuation by simply rescaling the remaining component by a factor of $\sqrt{3}$. Creutz ratios are then computed with this "abelianized" configuration. We find that the Creutz ratios of loops constructed from abelianized links converge to the usual Creutz ratios in the scaling regime.