Wilson loop distributions, higher representations and centre dominance in SU(2)

Abstract

To help understand the centre dominance picture of confinement, we look at Wilson loop distributions in pure SU(2) lattice gauge theory. A strong coupling approximation for the distribution is developed to use for comparisons. We perform a Fourier expansion of the distribution: centre dominance here corresponds to suppression of odd terms beyond the first. The Fourier terms correspond to SU(2) representations; hence Casimir scaling behaviour leads to centre dominance. We examine the positive plaquette model, where only thick vortices are present. We show that a simple picture of random, non-interacting centre vortices gives a string tension about 3/4 of the measured value. Finally, we attempt to limit confusion about the adjoint representation.

Center projection with and without gauge fixing

“…However, this agreement can actually be explained in a simple way, as shown in ref. [1] (see also [5,6]). …”

⟨A2⟩condensate, Bianchi identities, and chromomagnetic field degeneracy in SU(2) Yang-Mills theory

“…Ref. [47] and references therein), it seems that only Refs. [48,49] studied their relative orientations.…”

“…Let us consider first the behavior of the densities (47), (48) the density ρ falls down exponentially with γ and becomes of order O(10 −4 ) in D=3 (O(10 −3 ) in D=4). We note in passing that the mean plaquette 1/2 Tr U p is also almost insensitive to the γ coupling (Figure 7, bottom) rising in D=3 from 0.8248(1) to 0.8263(3) when γ is changed in the entire range (the corresponding change in D=4 is from 0.6301(2) to 0.6548(2)).…”

SU(3) vortex-like configurations in the maximal center gauge

“…The maximal center gauge is widely used to study low energy phenomena such as the confinement property or the breaking of the chiral symmetry, as can be seen in a set of recent works [1][2][3][4][5][6][7][8][9] and also in these proceedings. Nevertheless, at least to our knowlegde, there was no efficient method of direct gauge fixing to maximal center gauge in SU(N) lattice gauge theory for values N > 2.…”

“…We apply this new method to previously prepared SU(3) vortex-like configurations. Our purpose in the second part of this work is to know how these configurations look like in the maximal center gauge, and therefore, whether these solutions have the properties described in references [1][2][3][4][5][6][7][8][9] for a confining object. For a more detailed description of our results see reference [10].…”