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The thick center vortex model is applied to G(2) gauge group to obtain the potentials between static sources of the fundamental and adjoint representations. The group G(2) has only one trivial center element and therefore it does not have any vortices which are defined based on non trivial center elements. To obtain the potential from the thick center vortex model, the idea of the vacuum domain structure is used. The intermediate string tensions from this model are in rough agreement with the G(2) lattice results and the Casimir ratio. We argue that the SU(3) subgroup of G(2) may be responsible for the linear potential at the intermediate distances.Comment: 3 pages, 3 figures; talk given at the conference "Quark Confinement and the Hadron Spectrum IX", Madrid, Spain, 30th of August-3rd of September 2010; submitted to the proceedings, References adde

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The confinement problem is studied using the thick center vortex model. It is shown that the [Formula: see text] Cartan subalgebra of the decomposed [Formula: see text] gauge theory can play an important role in the confinement. The Casimir eigenvalues and ratios of the [Formula: see text] representations are obtained using its decomposition to the [Formula: see text] subgroups. This leads to the conjecture that the [Formula: see text] subgroups also can explain the [Formula: see text] properties of the confinement. The thick center vortex model for the [Formula: see text] subgroups of the [Formula: see text] gauge theory is applied without the domain modification. Instead, the presence of two [Formula: see text] vortices with opposite fluxes due to the possibility of decomposition of the [Formula: see text] Cartan subalgebra to the [Formula: see text] groups can explain the properties of the confinement of the [Formula: see text] group both at intermediate and asymptotic distances which is studied here.

We try to calculate the interaction between vortices in the color-flavor locked (CFL) phase of Quantum Chromodynamics (QCD). The most fundamental strings in high density color superconductivity are the non-abelian semi-super fluid strings. Using Abrikosov ansatz, one can show that the interaction between these vortices has a universal repulsion form when they are far from each other. The Ginzburg-Landau (GL) Lagrangian of CFL phase may be compared with the Lagrangian of Quantum Electrodynamics (QED) with three condensation states. The behavior of vortices of multi-component superconductivity, within the framework of GL theory was done for two condensation states (MgB 2 superconductors) by variational method. The interaction between these vortices is attractive when they are far from each other and repulsive when they get close.