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Using the lattice gauge field theory, we study the relation among the localchiral condensate, monopoles, and color magnetic fields in quantumchromodynamics (QCD). First, we investigate idealized Abelian gauge systems of1) a static monopole-antimonopole pair and 2) a magnetic flux withoutmonopoles, on a four-dimensional Euclidean lattice. In these systems, wecalculate the local chiral condensate on quasi-massless fermions coupled to theAbelian gauge field, and find that the chiral condensate is localized in thevicinity of the magnetic field. Second, using SU(3) lattice QCD Monte Carlocalculations, we investigate Abelian projected QCD in the maximally Abeliangauge, and find clear correlation of distribution similarity among the localchiral condensate, monopoles, and color magnetic fields in the Abelianizedgauge configuration. As a statistical indicator, we measure the correlationcoefficient $r$, and find a strong positive correlation of $r \simeq 0.8$between the local chiral condensate and an Euclidean color-magnetic quantity${\cal F}$ in Abelian projected QCD. The correlation is also investigated forthe deconfined phase in thermal QCD. As an interesting conjecture, likemagnetic catalysis, the chiral condensate is locally enhanced by the strongcolor-magnetic field around the monopoles in QCD.

Local correlation among the chiral condensate, monopoles, and color magnetic fields in Abelian projected QCD