Chiral Symmetry and BRST Symmetry Breaking, Quaternion Reality and the Lattice Simulation

TL;DR

This paper explores the interplay of chiral and BRST symmetry breaking, quaternion reality, and lattice simulation results, proposing boundary conditions and gauge field correlations as key factors in infrared phenomena and confinement.

Contribution

It introduces a novel perspective linking boundary conditions, quaternion reality, and gauge field correlations to chiral symmetry breaking and confinement in lattice QCD.

Findings

Deviation of the Kugo-Ojima parameter explained by boundary conditions.

Chiral symmetry breaking manifests through correlated fermions on domain walls.

Relation established between lattice fixed points, conformal theories, and quaternion conditions.

Abstract

We discuss that the deviation of the Kugo-Ojima color confinement parameter $u(0)$ from -1 in the case of quenched lattice simulation and the consistency with -1 in the case of full QCD simulation could be attributed to the boundary condition defined by fermions inside the region of $r<1$fm. By using the domain wall fermion propagator in lattice simulation, we show that the chiral symmetry breaking in the infrared can become manifest when one assumes that the left-handed fermion on the left wall and the right-handed fermion on the right wall are correlated by a self-dual gauge field. The relation between the infrared fixed point of the running coupling measured in lattice simulations, the prediction of the BLM renormalization theory, the conformal field theory with use of the t'Hooft anomaly matching condition in non-SUSY supersymmetric theory and the quaternion real condition are discussed.