Center projection with and without gauge fixing

Abstract

We consider projections of SU(2) lattice link variables onto Z 2 center and U(1) subgroups, with and without gauge-fixing. It is shown that in the absence of gauge-fixing, and up to an additive constant, the static quark potential extracted from projected variables agrees exactly with the static quark potential taken from the full link variables; this is an extension of recent arguments by Ambjørn and Greensite, and by Ogilvie. Abelian and center dominance is essentially trivial in this case, and seems of no physical relevance. The situation changes drastically upon gauge fixing. In the case of center projection, there are a series of tests one can carry out, to check if vortices identified in the projected configurations are physical objects. All these criteria are satisfied in maximal center gauge, and we show here that they all fail in the absence of gauge fixing. The non-triviality of center projection is due entirely to the maximal center gauge-fixing, which pumps information about the location of extended physical objects into local Z 2 observables.

First evidence for center dominance in SU(3) lattice gauge theory

“…Recently we have argued that center dominance by itself does not prove the role of center degrees of freedom in QCD dynamics [20,6]; some sort of center dominance exists also without any gauge fixing and can hardly by attributed to center vortices. Distinctive features of center- (4) and its error is shown in grey.…”

“…Recently, the center-vortex picture of confinement has found remarkable confirmation in numerical simulations of the SU(2) lattice gauge theory [3,4,5,6,7,8,9,10,11,12]. Our group has proposed a technique for locating center vortices in thermalized lattice configurations based on fixing to the so called maximal center gauge, followed by center projection [3,4,5].…”

“…It has also been demonstrated recently that removal of center vortices not only removes the asymptotic string tension, but restores chiral symmetry as well, and the SU(2) lattice is then brought to trivial topology [7]. The vortex density has been seen to scale as predicted by asymptotic freedom [8,5,6]. The properties of vortices have also been studied at finite temperature [9,10,11], and it has been argued that the non-vanishing string tension of spatial Wilson loops in the deconfined phase can be understood in terms of vortices winding through the periodic time direction.…”

Deconfinement in SU(2) Yang-Mills theory as a center vortex percolation transition

“…one finds a gauge-invariant type of center dominance (see [20] for the SU(2) theory and [21] for the SU(3) theory). Subsequently, it has been noted that this type of center dominance without gauge fixing can in fact be understood in quite simple terms [22], and that furthermore the density of center vortices arising on center-projected lattices without gauge fixing does not exhibit the renormalization group scaling corresponding to a finite physical density [23].…”

Gauge invariant Z(2) vortex vacuum textures and the SU(2) gluon condensate

“…Subsequently, it turned out that center projection even without previous gauge fixing reproduces the QQ potential, also at short distances, a finding which has somewhat obscured the relevance of the P -vortices for forming the string tension [20]. Moreover, in this case it was observed that other properties of the corresponding vortices (rather than the purely topological features) strongly depend on the bare lattice coupling constant (i.e.…”