[Paper Review] Evidence that centre vortices underpin dynamical chiral symmetry breaking in $\mathrm{SU}(3)$ gauge theory

Daniel Trewartha, Waseem Kamleh+1 more|arXiv (Cornell University)|Feb 24, 2015

Quantum Chromodynamics and Particle Interactions32 references4 citations

TL;DR

This study demonstrates that centre vortices are essential for dynamical chiral symmetry breaking in SU(3) lattice gauge theory, using overlap fermions to reveal that removing centre vortices eliminates chiral symmetry breaking. The results show that vortex-only backgrounds retain the capacity to generate dynamical mass after smoothing, indicating that centre vortices host the structural degrees of freedom necessary for instanton-like configurations and chiral symmetry breaking.

ABSTRACT

The link between dynamical chiral symmetry breaking and centre vortices in the gauge fields of pure $\mathrm{SU}(3)$ gauge theory is studied using the overlap-fermion quark propagator in Lattice QCD. Overlap fermions provide a lattice realisation of chiral symmetry and consequently offer a unique opportunity to explore the interplay of centre vortices, instantons and dynamical mass generation. Simulations are performed on gauge fields featuring the removal of centre vortices, identified through gauge transformations maximising the center of the gauge group. In contrast to previous results using the staggered-fermion action, the overlap-fermion results illustrate a loss of dynamical chiral symmetry breaking coincident with vortex removal. This result is linked to the overlap-fermion's sensitivity to the subtle manner in which instanton degrees of freedom are compromised through the process of centre vortex removal. Backgrounds consisting solely of the identified centre vortices are also investigated. After smoothing the vortex-only gauge fields, we observe dynamical mass generation on the vortex-only backgrounds consistent within errors with the original gauge-field ensemble following the same smoothing. Through visualizations of the instanton-like degrees of freedom in the various gauge-field ensembles, we find evidence of a link between the centre vortex and instanton structure of the vacuum. While vortex removal destabilizes instanton-like objects under ${\cal O}(a^4)$-improved cooling, vortex-only backgrounds provide gauge-field degrees of freedom sufficient to create instantons upon cooling.

Motivation & Objective

• To investigate the role of centre vortices in dynamical chiral symmetry breaking within pure SU(3) gauge theory.
• To resolve discrepancies between previous staggered-fermion results and the expected behavior of chiral symmetry using a more accurate fermion formulation.
• To determine whether centre vortices alone can sustain dynamical mass generation and support instanton-like structures.
• To examine how vortex removal affects the stability and structure of instanton-like configurations in the vacuum.

Proposed method

• Employing overlap fermions to preserve chiral symmetry on the lattice, enabling precise study of chiral symmetry breaking.
• Using gauge transformations that maximize the centre of the gauge group to identify and remove centre vortices from gauge field configurations.
• Comparing quark propagators from full gauge ensembles and vortex-removed ensembles to assess chiral symmetry breaking.
• Constructing and analyzing gauge field backgrounds composed solely of identified centre vortices.
• Applying ${\cal O}(a^4)$-improved cooling to vortex-only backgrounds to test the emergence of instanton-like structures.
• Visualizing instanton-like degrees of freedom across different gauge field ensembles to probe the vortex-instanton connection.

Experimental results

Research questions

• RQ1 Does the removal of centre vortices lead to a loss of dynamical chiral symmetry breaking in SU(3) gauge theory?
• RQ2 How do centre vortices influence the structure and stability of instanton-like configurations in the QCD vacuum?
• RQ3 Can gauge field configurations composed solely of centre vortices generate dynamical mass after smoothing?
• RQ4 To what extent do centre vortices host the degrees of freedom necessary for chiral symmetry breaking?
• RQ5 How does the choice of fermion action (overlap vs. staggered) affect the observed sensitivity to vortex removal?

Key findings

• Removal of centre vortices results in a complete loss of dynamical chiral symmetry breaking, as evidenced by the quark propagator in overlap-fermion simulations.
• Vortex-only gauge field backgrounds, after smoothing, generate dynamical mass consistent within errors to the original full ensemble, indicating that vortices alone support mass generation.
• The process of vortex removal destabilizes instanton-like configurations under ${\cal O}(a^4)$-improved cooling, suggesting that vortices are crucial for their formation.
• Visualizations reveal a direct structural link between centre vortices and the emergence of instanton-like degrees of freedom in the vacuum.
• The overlap-fermion formulation reveals a sensitivity to subtle changes in instanton structure upon vortex removal, explaining discrepancies with earlier staggered-fermion studies.
• Vortex-only backgrounds are sufficient to produce instanton-like objects upon cooling, demonstrating that centre vortices contain the essential topological structure for such configurations.