Lattice monopole action in pure SU(3) QCD

TL;DR

This paper derives an almost perfect monopole action in pure SU(3) lattice QCD, demonstrating monopole condensation and deriving a string model for the static potential, with implications for understanding confinement.

Contribution

It introduces a numerical and analytical approach to derive a perfect monopole action and static potential in SU(3) lattice QCD, connecting monopole dynamics to string models.

Findings

Monopole condensation occurs at large physical scales.

Two-point monopole interactions dominate at large scales.

The derived string model estimates the static potential and string tension.

Abstract

We obtain an almost perfect monopole action numerically after abelian projection in pure SU(3) lattice QCD. Performing block-spin transformations on the dual lattice, the action fixed depends only on a physical scale b. Monopole condensation occurs for large b region. The numerical results show that two-point monopole interactions are dominant for large b. We next perform the block-spin transformation analytically in a simplified case of two-point monopole interactions with a Wilson loop on the fine lattice. The perfect operator evaluating the static quark potential on the coarse b-lattice are derived. The monopole partition function can be transformed into that of the string model. The static potential and the string tension are estimated in the string model framework. The rotational invariance of the static potential is recovered, but the string tension is a little larger than the physical one.