Properties of P-vortex and monopole clusters in lattice SU(2) gauge theory

TL;DR

This paper investigates the properties and geometry of P-vortices and monopoles in lattice SU(2) gauge theory, highlighting differences between cluster types and their action densities using various projection methods.

Contribution

It provides a detailed analysis of P-vortex and monopole clusters, including their action densities and geometric properties, using both direct and indirect maximal center projections.

Findings

Short clusters have higher action density than percolating clusters.

Percolating cluster surface appears random at short distances.

Action density depends on the shape of the cluster.

Abstract

We study the action and geometry of P-vortices, discriminating between the percolating and finite clusters. We also discuss the interrelation of the monopoles and P-vortices. To define P-vortices we use both the direct maximal center projection and indirect maximal center projection. We find, in particular, that the action density of the P-vortices in short clusters is substantially higher than in the percolating cluster. The surface of the percolating cluster appears random at short distances, with action density depending on the shape.