Block spin transformation on the dual lattice and monopole action

TL;DR

This paper investigates monopole effective actions in SU(2) and SU(3) QCD on the dual lattice, aiming to derive a perfect lattice action that accurately reproduces physical observables like the string tension.

Contribution

It introduces a monopole effective action derived from numerical simulations and discusses modifications needed for accurate physical predictions, including in SU(3) QCD.

Findings

Polyakov loop behavior near T_c is well reproduced

A small repulsive term improves string tension accuracy

Monopole action in SU(3) expressed by a single monopole current

Abstract

To find a perfect lattice action in terms of monopole action on the dual lattice, we performed simulations of a monopole effective action obtained numerically from vacuum configurations in SU(2) QCD. Although the Polyakov loop behavior near $T_c$ is well reproduced by the action, a small but repulsive term is needed in addition to get the string tension correctly. It is reported also a monopole effective action in $SU(3)$ QCD which is expressed by one kind of monopole currents.