Abstract
In this paper, we study the role of the domain structure of the Yang Mills vacuum. The Casimir scaling and $N$-ality are investigated in the potentials between static sources in various representations for $SU(2)$ and $SU(3)$ gauge groups based on the domain structure model using square ansatz for angle $\alpha_{C}(x)$. We also discuss about the contributions of the vacuum domain and center vortices in the static potentials. As a result, the potentials obtained from vacuum domains agree with Casimir scaling better than the ones obtained from center vortices. The reasons of these observations are investigated by studying the behavior of the potentials obtained from vacuum domains and center vortices and the properties of the group factors. Then, the vacuum domains in $SU(N)$ and $G(2)$ gauge groups are compared and we argue that the $G(2)$ vacuum is filled with center vortices of its subgroups.
Highlights
Using thin center vortex model, one gets an area law for the potential of the quarks in the fundamental representation but not for the adjoint representation
The Casimir scaling and N -ality are investigated in the potentials between static sources in various representations for SU(2) and SU(3) gauge groups based on the domain structure model using square ansatz for angle αC(x)
We study the potentials between static sources and the behavior of the group factor Gr(α(n)) especially in SU(2) gauge group to investigate the contribution of the center domains
Summary
The vacuum is assumed to be filled with domain structures. In SU(N ) gauge group, there are N types of center domains including center vortices corresponding to the. N −1} are the Cartan generators, angle α(n) shows the flux profile that depends on the location of the nth center domain with respect to the Wilson loop, and dr is the dimension of the representation r. Where k is the N -ality of the representation r and if the core is entirely outside the minimal area of the loop, the group factor is equal to 1. 2. If the minimal area of the Wilson loop is pierced by a center domain, αC(x) = αmax, where αmax is obtained from the following maximum flux condition: exp(iαmax · Hr) = ei2kπn/N I. The only constraint is that the total color magnetic fluxes of the subregions must correspond to an element of the gauge group center.
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