# Monopole action and monopole condensation in SU(3) lattice QCD

## TL;DR

This paper derives effective monopole actions in SU(3) lattice QCD, analyzing monopole condensation and phase transitions at zero and finite temperatures, revealing insights into the confinement mechanism and fixed points.

## Contribution

It introduces monopole actions for extended monopoles in SU(3) lattice QCD and investigates their properties across different temperatures and scales.

## Key findings

- Monopole condensation occurs via energy-entropy balance at zero temperature.
- Scaling behavior similar to SU(2) case is not yet observed in SU(3).
- Hysteresis observed around the critical temperature indicating phase transition.

## Abstract

Effective monopole actions for various extended monopoles are derived from vacuum configurations after abelian projection in the maximally abelian gauge in $T=0$ and $T\ne 0$ $SU(3)$ lattice QCD. The actions obtained appear to be independent of the lattice volume adopted. At zero temperature, monopole condensation is seen to occur from energy-entropy balance in the strong coupling region. Larger $\beta$ is included in the monopole condensed phase as more extended monopoles are considered. The scaling seen in the $SU(2)$ case is not yet observed. The renormalization flow diagram suggests the existence of an infrared fixed point. A hysteresis behavior is seen around the critical temperature in the case of the $T\ne 0$ action.