QCD Monopoles and Chiral Symmetry Breaking on SU(2) Lattice

Abstract

Pseudoscalar correlator is measured in a singular (monopole dominant) and a regular (photon dominant) parts of a maximal abelian field on SU(2) lattice. In the abelian field and its singular part, light pseudoscalar boson are observed similar to that in SU (2) field. On the other hand , the correlator in the regular part behaves like a product of free quark and anti-quark. Obtained results give a support for a possibility that monopole condensation is responsible for chiral symmetry breaking as well as confinement. Correlation between monopoles and instantons is also investigated by observing topological charge. A field including monopoles carrys topological charge with good correlation to that in original SU(2) gauge field while that including only photons shows no topological charge.

Topological aspect of Abelian projected SU(2) lattice gauge theory

“…Thus, these results shed new light on the non-trivial relation between instantons and QCD-monopoles. Recently, both analytic works [10,11] and numerical works [12,13,15,14,16] have shown the existence of the strong correlation between these topological objects in spite of the fact that they originate from different homotopy groups. Furthermore, monopole trajectories become more complicated with the instanton density increasing in the background of a random ensemble of instanton solutions [17].…”

Lattice study of UA(1) anomaly: the role of QCD-monopoles

“…Recently, some interesting results turn our attention to the non-trivial relation between instantons and magnetic monopoles [3][4][5][6][7][8][9][10]. As for the appearance of magnetic monopoles (QCD-monopoles) in SU(N c ) gauge theory, 't Hooft proposed a stimulating idea of the abelian gauge fixing [11].…”

“…However, the recent analytical works have demonstrated the QCD-monopole as a classically stable solution in the background fields of the instanton configuration using the abelian gauge fixing [3,4]. Furthermore, the several lattice simulations have shown the strong correlation between instantons and QCD-monopoles in the highly quantum vacuum [4][5][6][7][8] as well as the semi-classical vacuum [8][9][10]. Their interrelation brings us a conjecture that the presence of QCD-monopoles plays a considerable role on the U A (1) anomaly.…”

Abelian Projections and Monopoles

“…It is known that the (anti-) instantons produce abelian monopole currents [46]. The abelian monopole trajectories may go through the center of the instanton (Figure 14(a)) or form a circle around it (Figure 14(b)).…”