# Monopole Order Parameter in SU(2) Lattice Gauge Theory

## TL;DR

This paper provides numerical evidence for the existence of an abelian monopole condensate in SU(2) lattice gauge theory, supporting the dual superconductor model of confinement by analyzing monopole creation operators across phase transitions.

## Contribution

It offers the first numerical calculation of the monopole creation operator distribution in SU(2) lattice gluodynamics, confirming the monopole condensate in the confinement phase.

## Key findings

- Monopole creation operator distribution shifts below the phase transition.
- Effective potential is of Higgs type in the confinement phase.
- Supports the dual superconductor model of confinement.

## Abstract

We present the results of the numerical calculation of the probability distribution of the value of the monopole creation operator in $SU(2)$ lattice gluodynamics. We work in the maximal abelian projection. It occurs that at the low temperature, below the deconfinement phase transition the maximum of the distribution is shifted from zero, which means that the effective constraint potential is of the Higgs type. Above the phase transition the minimum of the potential (the maximum of the monopole field distribution) is at the zero value of the monopole field. This is the direct proof of the existence of the abelian monopole condensate in the confinement phase of the gluodynamics, which confirms the dual superconductor model of the confining vacuum.