Confinement in G(2) gauge theories using the thick center vortex model and domain structures

Abstract

The thick center vortex model with the idea of using domain structures is used to calculate the potentials between two G(2) heavy sources in the fundamental, the adjoint and the 27 dimensional representations. The potentials are screened at large distances. This behavior is expected from the thick center vortex model since G(2) has only a trivial center element which makes no contribution to the average Wilson loop at the large distance regime. A linear potential is obtained at intermediate distances for all representations. This behavior can be explained by the thickness of the vortices (domains) and by defining a flux for the trivial center element of G(2). The role of the SU(3) subgroup of G(2) in the linear regime is also discussed. The string tensions are in rough agreement with the Casimir operators of the corresponding representations.

Contributions of the center vortices and vacuum domain in potentials between static sources

“…However, the linear rise of the potentials for all representations at the intermediate distances was clearly observed in lattice gauge theory [18,26]. On the other hand, from the domain structure model, we have observed linear potentials between G(2) sources for different representations roughly proportional to the eigenvalue of the quadratic Casimir operator of the representation which is in agreement with the lattice results [27]. In our previous article [30], we have argued that the SU (2) and SU(3) subgroups of the G(2) gauge group may be responsible for the confinement potential of G (2).…”

“…The confinement regime has been increased [18] when the vacuum domains have been added to the model. In our previous papers [27,30], we have studied the role of the vacuum domain in G(2) gauge group which has one trivial center element, only. According to the center vortex theory, one does not expect confinement in a group without nontrivial center element.…”

Exceptional thermodynamics: the equation of state of G2 gauge theory

“…In fact, numerical simulations of this Yang-Mills theory have already been going on for some years [74][75][76][77][78][79][80][81][82][83][84][85]. Besides numerical studies, these peculiar features of G 2 Yang-Mills theory have also triggered analytical interest [86][87][88][89][90][91][92][93][94][95][96][97].…”

Confinement inF4Exceptional Gauge Group Using Domain Structures

“…Using the thick center vortex model with the idea of vacuum domain structures, Deldar et al have found the potential between static color sources in the G 2 gauge group [5], [6], [7]. Their results are compatible with numerical Lattice calculations for the G 2 gauge group [8], [9], [10], [11].…”