2017

DOI: 10.1051/epjconf/201713713013

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Confinement inF₄Exceptional Gauge Group Using Domain Structures

Shahnoosh Rafibakhsh

¹

,

²

Abstract: Abstract. We calculate the potential between static quarks in the fundamental representation of the F 4 exceptional gauge group using domain structures of the thick center vortex model. As non-trivial center elements are absent, the asymptotic string tension is lost while an intermediate linear potential is observed. SU(2) is a subgroup of

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So(9) Subgroup3

Confinement Without a Center1

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Cited by 2 publications

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“…After an initial review, the elements of these matrices are not fully the same as the corresponding ones in Eqs. ( 25) and ( 32) or (45). Accordingly, the trivial static potentials, when we consider trivial center element of the SU (2) subgroup, are not identical with the F 4 exceptional group itself.…”

Section: So(9) Subgroupmentioning

confidence: 97%

“…It should be recalled that matrices of Eq. (45), are normalized with the normalization condition in Eq. (17).…”

Section: Confinement Without a Centermentioning

confidence: 99%

“…We have investigated this subgroup in ref. [45]. However, it is another aspect of this decomposition which is appealing.…”

Section: So(9) Subgroupmentioning

confidence: 99%

“…As a result, although the matrices of Eqs. (45) and (60) have different elements and the potentials out of these two generators behave differently, the number of center vortices which emerge in both decompositions is the same. Thus, the group factor reaches the same minimum amount in both of them.…”

Section: So(9) Subgroupmentioning

confidence: 99%

See 3 more Smart Citations

F4 , E6 and
Shahlaei
¹
,
Rafibakhsh
²

2018
Phys. Rev. D
Self Cite
3
1
4
0
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Using vacuum domain structure model, trivial static potentials in various representations of F4, E6 and G2 exceptional groups are calculated by means of the unit center element. Due to the absence of the non-trivial center elements, the potential of every representation is screened at far distances. However, the linear part is observed at intermediate quark separations which is investigated by the decomposition of the exceptional group to its maximal subgroups. Comparing the group factor of the super-group with the corresponding one obtained from the non-trivial center elements of SU (3) subgroup, shows that SU (3) is not the direct cause of temporary confinement in any of the exceptional groups. However, the trivial potential obtained from the group decomposition to the SU (3) subgroup is the same as the potential of the super-group itself. In addition, any regular or singular decomposition to the SU (2) subgroup which produces the Cartan generator with the same elements as h1, in any exceptional group, leads to the linear intermediate potential of the exceptional gauge groups. The other SU (2) decompositions with the Cartan generator different from h1, are still able to describe the linear potential if the number of SU (2) non-trivial center element which emerge in the decompositions is the same. As a result, it is the center vortices quantized in terms of non-trivial center element of the SU (2) subgroup which give rise to the intermediate confinement in the static potentials.

“…After an initial review, the elements of these matrices are not fully the same as the corresponding ones in Eqs. ( 25) and ( 32) or (45). Accordingly, the trivial static potentials, when we consider trivial center element of the SU (2) subgroup, are not identical with the F 4 exceptional group itself.…”

Section: So(9) Subgroupmentioning

confidence: 97%

“…It should be recalled that matrices of Eq. (45), are normalized with the normalization condition in Eq. (17).…”

Section: Confinement Without a Centermentioning

confidence: 99%

“…We have investigated this subgroup in ref. [45]. However, it is another aspect of this decomposition which is appealing.…”

Section: So(9) Subgroupmentioning

confidence: 99%

“…As a result, although the matrices of Eqs. (45) and (60) have different elements and the potentials out of these two generators behave differently, the number of center vortices which emerge in both decompositions is the same. Thus, the group factor reaches the same minimum amount in both of them.…”

Section: So(9) Subgroupmentioning

confidence: 99%

See 2 more Smart Citations

F4 , E6 and
Shahlaei
¹
,
Rafibakhsh
²

2018
Phys. Rev. D
Self Cite
3
1
4
0
View full text Add to dashboard Cite

Using vacuum domain structure model, trivial static potentials in various representations of F4, E6 and G2 exceptional groups are calculated by means of the unit center element. Due to the absence of the non-trivial center elements, the potential of every representation is screened at far distances. However, the linear part is observed at intermediate quark separations which is investigated by the decomposition of the exceptional group to its maximal subgroups. Comparing the group factor of the super-group with the corresponding one obtained from the non-trivial center elements of SU (3) subgroup, shows that SU (3) is not the direct cause of temporary confinement in any of the exceptional groups. However, the trivial potential obtained from the group decomposition to the SU (3) subgroup is the same as the potential of the super-group itself. In addition, any regular or singular decomposition to the SU (2) subgroup which produces the Cartan generator with the same elements as h1, in any exceptional group, leads to the linear intermediate potential of the exceptional gauge groups. The other SU (2) decompositions with the Cartan generator different from h1, are still able to describe the linear potential if the number of SU (2) non-trivial center element which emerge in the decompositions is the same. As a result, it is the center vortices quantized in terms of non-trivial center element of the SU (2) subgroup which give rise to the intermediate confinement in the static potentials.

Accelerated discovery of machine-learned symmetries: Deriving the exceptional Lie groups G2, F4 and E6

Forestano,

Matchev,

Matcheva

et al. 2023

Physics Letters B

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