Properties of P-vortices and monopole clusters in latticeSU(2)gauge theory

Abstract

We study the action and geometry of P-vortices, discriminating between the percolating and finite clusters. We also discuss the interrelation of the monopoles and P-vortices. To define P-vortices we use both the direct maximal center projection and indirect maximal center projection. We find, in particular, that the action density of the P-vortices in short clusters is substantially higher than in the percolating cluster. The surface of the percolating cluster appears random at short distances, with action density depending on the shape.

Evidence for fine tuning of fermionic modes in lattice gluodynamics

“…One can show that the modification (16) affects (up to a gauge transformation) only a 3d fraction of the total 4d volume of the lattice [22]. In other words, this fraction is proportional to (a · Λ QCD ) and vanishes in the limit of a → 0.…”

Generation of confinement and other nonperturbative effects by infrared gluonic degrees of freedom

“…• Maximal Abelian gauge monopoles on vortices: While in the Laplacian center gauge, monopoles are located on vortices by construction, one also finds empirically that maximal Abelian gauge monopoles are located on maximal center gauge vortices [27,46]. Moreover, the action in the monopole region is not distributed isotropically, but is collimated in the directions of the vortex.…”

Center vortices as rigid strings

“…In real simulations about 95% of monopole trajectories belong to center vortices [19,20]. It is natural to conjecture that twodimensional field theory living on vortex surfaces should describe these monopoles upon first quantization.…”

“…In the section III this action is discussed as an effective action induced by some two-dimensional fields localized on the surfaces of vortices and a model-independent check of localization is performed. Monopoles in the Abelian projection of the theory [4,19,20] are then discussed as appropriate candidates for such localized fields in the section IV. The dependence of the bare string tension on the lattice spacing can be explained if one takes into account the contribution of percolating monopole cluster.…”