Confinement and broken global symmetries

In particle physics, two prominent phenomena are due to non-perturbative interactions. One is the absence of fundamental particles from the observable spectrum, in particular quarks and gluons. This phenomenon is called confinement. The other is the breaking of (global) symmetries, like chiral symmetry or the electroweak symmetry, giving mass to the particles. These two effects shape the world around us, as they determine which particles are observable and what their mass is. These phenomena are likely related. In particular for the breaking of chiral symmetry and confinement, this has been investigated to great extent and in great detail. This is less apparent for the case of broken global gauge symmetries. However, there are general arguments that the physical spectrum is not changed by the breaking of global gauge symmetries for systems like the weak sector of the standard model. Therefore confinement, which influences this spectrum, and the breaking of these symmetries are likely related as well. In all cases the link is mediated by the coupling of matter fields to a non-Abelian gauge field. The aim of this project is to investigate the existence and properties of such a link in detail. This will be done by determining the properties of the elementary degrees of freedom of quarks, gauge bosons and Higgs particles. E.g., the eigenspectrum of the Dirac operator, which governs the propagation of quarks, contains information on their confinement as well as on chiral symmetry breaking. It will therefore grant access to these phenomena. Correlation functions of gauge bosons and Higgs particles will, on the other hand, provide information on their presence in the physical spectrum as well as on how the breaking of global symmetries manifest themselves. An interesting observation here is that the pattern of relations between confinement and the breaking of global symmetries changes depending on the charge structure of the matter fields. If they carry charge in the fundamental representation of the gauge group, like the quarks and the Higgs, the link between the broken symmetries and confinement seems to be rather strong. If the matter fields carry charges in the adjoint representation, i.e., the same type of charge as the gauge bosons, there seems to be no direct link between both phenomena. By comparing both cases, it will be investigated whether these are in fact unrelated, or whether the link is just less apparent. These quantities will be extracted primarily using lattice gauge theory and, when useful, also using functional methods like the quantum equations of motion. These investigations are of course interesting also from another point of view: FAIR, to be constructed at GSI, and the LHC at CERN will be used to investigate these phenomena and their relation experimentally during the next decades. Theoretical insight into confinement, breaking of global symmetries, and the relation between them will therefore be of great importance.