<p>One of the still big problems in the Standard Model of particle physics is the problem of confinement. Quarks or other coloured particles have never been observed in isolation. Quarks are only observed in colour neutral bound states. The strong interactions are described using a Yang-Mills theory. These type of theories exhibits asymptotic freedom, i.e. the coupling is weak at high energies. This means that the theory is perturbative at high energies only. Understanding quark confinement requires knowledge of the non perturbative regime. One attempt has been to identify the proper order parameters for describing the low energy limit and then to write down effective actions in terms of these order parameters. We discuss one possible scenario for confinement and the effective models constructed with this as inspiration. Further we discuss solitons in these models and their properties.</p><p>Yang-Mills theory has also become important in the context of string theory. According to the AdS/CFT correspondence string theory in AdS₅×S⁵ is dual to four dimensional Yang-Mills with four supersymmetries. The duality relate the non perturbative regime of one of the theories to the perturbative regime of the other. This makes it in general hard to test this conjecture. For a special type of solutions it is however possible to use a perturbative expansion in both theories. We discuss this type of solutions and in particular we discuss a method, the Bethe ansatz, to find the solutions on the gauge theory side.</p>

One of the still big problems in the Standard Model of particle physics is the problem of confinement. Quarks or other coloured particles have never been observed in isolation. Quarks are only observed in colour neutral bound states. The strong interactions are described using a Yang-Mills theory. These type of theories exhibits asymptotic freedom, i.e. the coupling is weak at high energies. This means that the theory is perturbative at high energies only. Understanding quark confinement requires knowledge of the non perturbative regime. One attempt has been to identify the proper order parameters for describing the low energy limit and then to write down effective actions in terms of these order parameters. We discuss one possible scenario for confinement and the effective models constructed with this as inspiration. Further we discuss solitons in these models and their properties. Yang-Mills theory has also become important in the context of string theory. According to the AdS/CFT correspondence string theory in AdS5×S5 is dual to four dimensional Yang-Mills with four supersymmetries. The duality relate the non perturbative regime of one of the theories to the perturbative regime of the other. This makes it in general hard to test this conjecture. For a special type of solutions it is however possible to use a perturbative expansion in both theories. We discuss this type of solutions and in particular we discuss a method, the Bethe ansatz, to find the solutions on the gauge theory side.