Universality check of Abelian monopoles

Abstract

We study the Abelian projected SU(2) lattice gauge theory after gauge fixing to the maximally Abelian gauge (MAG). In order to check the universality of the Abelian dominance we employ the tadpole improved tree level (TI) action. We show that the density of monopoles in the largest cluster (the IR component) is finite in the continuum limit which is approximated already at relatively large lattice spacing. The value itself is smaller than in the case of Wilson action. We present results for the ratio of the Abelian to non-Abelian string tension for both Wilson and TI actions for a number of lattice spacings in the range 0.06 fm < a < 0.35 fm. These results show that the ratio is between 0.9 and 0.95 for all considered values of lattice couplings and both actions. We compare the properties of the monopole clusters in two gauges -in MAG and in the Laplacian Abelian gauge (LAG). Whereas in MAG the infrared component of the monopole density shows a good convergence to the continuum limit, we find that in LAG it is even not clear whether a finite limit exists.

Determination of the properties of vector mesons in external magnetic field by quenched SU(3) lattice QCD

“…8) where S pl,rt = (1/2)Tr(1 − U pl,rt ) is the plaquette (denoted by pl) or 1×2 rectangular loop term (rt), u 0 = (W 1×1 ) 1/4 = (1/2)TrU pl 1/4 is the input tadpole factor computed at zero temperature [35]. This action suppresses ultraviolet dislocations which leads to non-physical near-zero modes of the Wilson-Dirac operator and difficulties in choice of the ρ parameter (see subsection 2.1).…”

Calorons and dyons at the thermal phase transition analyzed by overlap fermions

“…For SU (2) gauge theory, the tadpole factor u 0 has been selfconsistently determined first in Ref. [67] for a few β imp values in the case of vanishing temperature on L 4 lattices with a suitable lattice size L for each value of the bare coupling constant. The result is given in Table I.…”

“…We employ for the actual analysis of the caloron/dyon content of SU (2) gauge theory the tadpole improved action of the Lüscher-Weisz form [66,67] …”

Interrelation between monopoles, vortices, topological charge, and chiral symmetry breaking: Analysis using overlap fermions forSU(2)

“…For comparison, we recall an estimate [33] of the monopole density at T = 0 for β imp = 3.25 and the same action: ρ mon a 3 = 0.0126 (1). That means that the monopole density is only insignificantly suppressed at T dec compared to T = 0.…”

“…The presence of both components becomes obvious in studies of universality [33] where only the infrared part possesses a finite continuum limit that can be compared between different actions. This problem will show up in the process of smearing discussed in section IV.…”