A model of random center vortex lines in continuous 2+1-dimensional space-time

TL;DR

This paper introduces a continuous 2+1D center vortex model with random closed lines, exploring confinement and deconfinement phases without lattice scaffolding, using Monte Carlo simulations to analyze vortex behavior and phase transitions.

Contribution

It presents a novel continuous-space vortex model with variable vortex numbers and reconnections, advancing understanding of confinement mechanisms in QCD.

Findings

Identified three distinct deconfinement phase transitions.

Demonstrated the impact of vortex density and segment length on confinement.

Showed the model reproduces key features of QCD confinement and deconfinement.

Abstract

A picture of confinement in QCD based on a condensate of thick vortices with fluxes in the center of the gauge group (center vortices) is studied. Previous concrete model realizations of this picture utilized a hypercubic space-time scaffolding, which, together with many advantages, also has some disadvantages, e.g., in the treatment of vortex topological charge. In the present work, we explore a center vortex model which does not rely on such a scaffolding. Vortices are represented by closed random lines in continuous 2+1-dimensional space-time. These random lines are modeled as being piece-wise linear, and an ensemble is generated by Monte Carlo methods. The physical space in which the vortex lines are defined is a torus with periodic boundary conditions. Besides moving, growing and shrinking of the vortex configurations, also reconnections are allowed. Our ensemble therefore contains not a fixed, but a variable number of closed vortex lines. This is expected to be important for realizing the deconfining phase transition. We study both vortex percolation and the potential V (R) between quark and anti-quark as a function of distance R at different vortex densities, vortex segment lengths, reconnection conditions and at different temperatures. We find three deconfinement phase transitions, as a function of density, as a function of vortex segment length, and as a function of temperature.