Abstract
The centre vortex structure of the $SU(3)$ gauge field vacuum is explored through the use of novel visualisation techniques. The lattice is partitioned into 3D time slices, and vortices are identified by locating plaquettes with nontrivial centre phases. Vortices are illustrated by rendering vortex lines that pierce these nontrivial plaquettes. Nontrivial plaquettes with one dimension in the suppressed time direction are rendered by identifying the visible spatial link. These visualisations highlight the frequent presence of singular points and reveal an important role for branching points in $SU(3)$ gauge theory in creating high topological charge density regimes. Visualisations of the topological charge density are presented, and an investigation into the correlation between vortex structures and topological charge density is conducted. The results provide new insight into the mechanisms by which centre vortices generate nontrivial gauge field topology. This work demonstrates the utility of visualisations in conducting centre vortex studies, presenting new avenues with which to investigate this perspective of the QCD vacuum.
Highlights
In recent years the center vortex perspective of the QCD vacuum [1,2] has emerged as the most fundamental aspect of QCD vacuum structure, simultaneously governing the properties of confinement and dynamical chiral symmetry breaking in quantum chromodynamics (QCD)
In this work we have presented a new way to examine the four-dimensional structure of center vortices on the lattice through the use of 3D visualization techniques
We have explored the connection between these vortex structures and topological charge density
Summary
In recent years the center vortex perspective of the QCD vacuum [1,2] has emerged as the most fundamental aspect of QCD vacuum structure, simultaneously governing the properties of confinement and dynamical chiral symmetry breaking in quantum chromodynamics (QCD). Intimately to the geometry of vortices in the vacuum indicates that visualizing these structures may provide valuable insight [19,20] To this end, we construct visualizations of center vortices and topological charge density on the lattice. We construct visualizations of center vortices and topological charge density on the lattice We use these visualizations to investigate the dynamics of the vortex model in an interactive and novel manner. In the Supplemental Material [21] these visualizations are presented as interactive 3D models embedded in the document. VIII we investigate the correlation these structures have with topological charge density This investigation lays the groundwork for the development of further visualization techniques and emphasizes the importance of center vortex geometry in a full understanding of the QCD vacuum
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